Lawmakers will resume counting votes on Wednesday, hours after the Capitol building was cleared. Senators and members of the House had evacuated when Trump supporters disrupted Congress’s debate of President-elect Joe Biden’s victory.

Congress is set to resume counting tonight, Pelosi says, hours after mob takes control of the Capitol.

Biden calls on Trump to go on national television and ‘demand an end to this siege.’

McConnell rebukes Trump for efforts to overturn the election, warning of a ‘death spiral’ of democracy.

Lawmakers will resume counting Electoral College votes on Wednesday, hours after a mob of Trump loyalists stormed the Capitol, Speaker Nancy Pelosi of California said as she vowed that the attack would not “deter us from our responsibility to validate the election of Joe Biden.”

In a letter to colleagues, Ms. Pelosi said she had reached that decision after consulting with her leadership team and a series of calls with the Pentagon, the Justice Department and Vice President Mike Pence. She made no mention of the president.

“We always knew this responsibility would take us into the night,” Ms. Pelosi wrote. “We also knew that we would be a part of history in a positive way today, despite ill-founded objections to the Electoral College vote. We now will be part of history, as such a shameful picture of our country was put out to the world, instigated at the highest level.”

Violence overtook the Capitol on Wednesday afternoon, when a mob of people loyal to President Trump stormed the building, halting Congress’s counting of the electoral votes as the police evacuated lawmakers from the building in a scene of violence, chaos and disruption that shook the core of American democracy.

The sergeant-at-arms, the top security official at the Capitol, announced that the building had been secured around 5:40 p.m.

The unrest prompted Mayor Muriel Bowser of Washington to declare a citywide curfew from 6 p.m. Wednesday night to 6 a.m. Thursday morning. The Army is activating the entire District of Columbia National Guard — 1,100 troops — in response to a request from the mayor, an Army official said on Wednesday.

The chaos began around 2:15 p.m., as the House and Senate debated a move by a faction of Republicans to overturn the election results, security rushed Vice President Mike Pence out of the Senate chamber and the Capitol building was placed on lockdown after angry pro-Trump demonstrators surged past barricades and law enforcement toward the legislative chambers.

For a time, senators and members of the House were locked inside their respective chambers. Images posted on social media showed scenes of supporters violently tussling with the police as at least one person took to the rostrum of the House chamber to declare his support for Mr. Trump.

A woman, who seemed to be part of the group that stormed the Capitol, can be seen in a video posted on social media being shot inside the building. She was in critical condition with a wound to the neck, The Associated Press reported.

“This is what you’ve gotten, guys,” Senator Mitt Romney, Republican of Utah, yelled as the mayhem unfolded in the Senate chamber, apparently addressing his colleagues who were leading the charge to press Mr. Trump’s false claims of a stolen election.

Mr. Biden responded to the violence on Wednesday, saying, “I call on President Trump to go on national television now to fulfill his oath and defend the Constitution and demand an end to this siege.”

In a brief video posted to his Twitter account shortly after 4 p.m., Mr. Trump repeated his baseless claim that “the election was stolen” and spoke in sympathetic and affectionate terms to members of the mob, advising them to “go home,” adding, “We love you.”

The posting came hours after Mr. Trump appeared at a rally in which he exhorted his supporters to go to the Capitol to register their discontent. Earlier in the afternoon, Mr. Trump tweeted statements intended to tamp down on the violence.

“Please support our Capitol Police and Law Enforcement,” he posted. “They are truly on the side of our Country. Stay peaceful!”

As the clashes intensified, he tweeted: “I am asking for everyone at the U.S. Capitol to remain peaceful. No violence! Remember, WE are the Party of Law & Order — respect the Law and our great men and women in Blue.”

The extraordinary day in Washington laid bare deep divisions both between the two parties and within Republican ranks, when the ceremonial counting of electoral votes that unfolds every four years in Congress turned into an explosive spectacle, with Mr. Trump stoking the unrest.

Democratic lawmakers said the Capitol Police had instructed them to take cover on the floor and prepare to use gas masks after tear gas was dispersed in the Capitol Rotunda.

On the other side of the Capitol, Representative Steve Cohen, Democrat of Tennessee, yelled out to Republicans on the House floor: “Call Trump, tell him to call off his revolutionary guards.”

In a scene of unrest common in other countries but seldom witnessed in the history of the United States capital, hundreds of people in the mob barreled past fence barricades outside the Capitol and clashed with officers. Shouting demonstrators mobbed the second floor lobby just outside the Senate chamber, as law enforcement officials placed themselves in front of the chamber doors.

[banging on door] [yelling] “This way! This way! This way! This way!” “They broke the glass?” “Everybody stay down, get down!” [crowd noise] [shot fired] “Take that House, take it now! Take it now!” [flash bang] [crowd noise] “You ain’t gonna stop us!” [flash bang] [crowd noise]

Multiple lawmakers reported that the Capitol Police had instructed them to take cover on the House floor and prepare to use gas masks after tear gas was dispersed in the Capitol Rotunda of the Capitol. Shortly afterward, the police escorted senators and members of House from the building to others nearby, as the mob swarmed the hallways just steps from where lawmakers were meeting, carrying pro-Trump paraphernalia.

Representative Nancy Mace, a freshman Republican from South Carolina, described seeing people “assaulting Capitol Police.” In a Twitter post, Ms. Mace shared a video of the chaos and wrote, “This is wrong. This is not who we are. I’m heartbroken for our nation today.”

Just evacuated my office in Cannon due to a nearby threat. Now we’re seeing protesters assaulting Capitol Police. This is wrong. This is not who we are. I’m heartbroken for our nation today.

Other Republican lawmakers, locked inside the Capitol, used Twitter to urge the mob to be peaceful.

And later on Wednesday evening, former President George W. Bush was also among the high-profile Republicans who sharply condemned what he called “mayhem” and a “violent assault on the Capitol.”

“This is how election results are disputed in a banana republic — not our democratic republic,” he said in a statement. “I am appalled by the reckless behavior of some political leaders since the election and by the lack of respect shown today for our institutions, our traditions, and our law enforcement.”

“Insurrection could do grave damage to our nation and reputation,” he added. “In the United States of America, it is the fundamental responsibility of every patriotic citizen to support the rule of law.”

In the early afternoon, the police fired what appeared to be flash-bang grenades. Rather than disperse, the demonstrators cheered and shouted, “push forward, push forward.” One person shouted, “that’s our house,” meaning the Capitol. Other people repeatedly shouted, “You swore an oath.”

As officers and members of the mob clashed outside, lawmakers had been debating an objection to the certification of Arizona electors, ensconced in their respective chambers. Senator Mitch McConnell, Republican of Kentucky and the majority leader, warned of a “death spiral” for democracy, while Representative Jim Jordan, Republican of Ohio, listed a litany of accusations of election fraud with little evidence.

“I don’t recognize our country today, and the members of Congress who have supported this anarchy do not deserve to represent their fellow Americans,” said Representative Elaine Luria, Democrat of Virginia.

Thank you to Capitol Police for protecting the People’s House.Protesters have a Constitutionally-protected right to be heard, but I urge them to remain peaceful.

Our democracy is under unprecedented assault — unlike anything we’ve seen in modern times. An assault on the citadel of liberty, the Capitol itself. I call on this mob to pull back and allow the work of democracy to go forward. You’ve heard me say it before in a different context, the words of a president matter, no matter how good or bad that president is. I call on President Trump to go on national television, now, to fulfill his oath, and defend the Constitution. And demand an end to this siege. It’s not a protest, it’s insurrection. The world is watching. Like so many other Americans, I am genuinely shocked and saddened that our nation, so long the beacon of light and hope for democracy, has come to such a dark moment. Notwithstanding what I saw today, what we’re seeing today, I remain optimistic about the incredible opportunities. There’s never been anything we can’t do when we do it together. So President Trump, step up.

President-elect Joseph R. Biden Jr. demanded on Wednesday that President Trump call on his supporters to end what Mr. Biden called an “unprecedented assault” on democracy as an angry mob breached the Capitol, delaying the formal certification of the 2020 election and plunging Washington into chaos.

“I call on President Trump to go on national television now to fulfill his oath and defend the Constitution and demand an end to this siege,” Mr. Biden said in brief remarks from Wilmington, Del.

Seeking to tamp down the anarchy that Mr. Trump stoked with angry rhetoric just hours earlier, Mr. Biden urged rioters to abandon what amounted to an armed occupation of the House and Senate. The president-elect denounced Mr. Trump’s refusal to graciously accept defeat, and suggested that the president was to blame for the violence.

“At their best, the words of a president can inspire,” Mr. Biden said. “At their worst, they can incite.”

He added: “This is not dissent. It’s disorder. It’s chaos. It borders on sedition, and it must end now. I call on this mob to pull back and allow the work of democracy to go forward.”

Violent clashes between the police and a pro-Trump mob underscored a grim reality for Mr. Biden: He will not only inherit a country wracked by a pandemic and an economic crisis, but also a political fabric that has been ripped apart by Mr. Trump in ways that have few equals in the nation’s history.

Never before in America’s modern history has the peaceful transfer of power devolved into a physical confrontation inside the corridors of power in Washington, this time egged on by an incumbent president, who on Wednesday morning raged that the election was “rigged” and vowed “we will never concede!”

Unlike Mr. Biden, Mr. Trump remained mostly silent for hours, tweeting only that he hoped his supporters would remain peaceful and eventually saying that the National Guard would be sent to help the police.

Moments after Mr. Biden delivered his remarks, Mr. Trump posted a one-minute video in which he empathized with the rioters because “we had an election that was stolen,” but urged them to “go home now. We have to have peace. We have to have law and order.”

But many of his supporters appeared to dismiss the president’s tweets and video. Protesters waving “TRUMP” flags descended on the Capitol.

Instead of delivering remarks about his plans to accelerate the country’s economic recovery, the president-elect delivered a forceful call for peace as the National Guard raced to Washington.

“At this hour our democracy is under unprecedented assault,” he said, adding later, “Today is a reminder, a painful one, that democracy is fragile.”

The Army is activating the entire District of Columbia National Guard — 1,100 troops — in response to a request from Mayor Muriel Bowser of Washington, an Army official said on Wednesday.

The troops are being sent to the D.C. Armory and will be deployed to the Capitol and to other points around Washington, the official said.

In a statement, Jonathan Hoffman, a Pentagon spokesman, said the Guard had been mobilized and the response would be led by the Justice Department. The decision by Army Secretary Ryan McCarthy and Christopher C. Miller, the acting defense secretary, came as protesters breached the Capitol.

Defense and administration officials said it was Vice President Mike Pence, not President Trump, who approved the order to deploy the D.C. National Guard. It was unclear why the president, who incited the protesters to storm the Capitol and who is still the commander in chief, did not give the order.

A Defense official said that 150 D.C. National Guard troops were en route to the Capitol at 5:20 p.m. to back up the police in clearing the area. The troops, the official said, would be wearing protective and riot gear but would not be armed, although that could change if the situation deteriorated Wednesday night. The troops would be stationed around the grounds of the Capitol to re-establish a perimeter.

Mr. Miller said on Wednesday afternoon that he had spoken with Mr. Pence, Speaker Nancy Pelosi, Senators Mitch McConnell and Chuck Schumer, and Representative Steny H. Hoyer of Maryland about the protests at the Capitol.

“We have fully activated the D.C. National Guard to assist federal and local law enforcement as they work to peacefully address the situation,” Mr. Miller said. “We are prepared to provide additional support as necessary and appropriate as requested by local authorities. Our people are sworn to defend the Constitution and our democratic form of government, and they will act accordingly.”

Mr. Hoffman noted that the troops were deploying in “support” of federal law enforcement in the district, reflecting Defense officials’ reluctance to send military troops to the Capitol. Defense officials want the authorities in Washington to use the local police and other law enforcement agencies to confront the protesters, with the National Guard troops in support but not in the lead, to avoid the specter of a military battling election protests.

But the tense standoff at the Capitol, and the breach by Trump supporters, led to the decision, officials said.

Bureau agents went to the Capitol grounds on Wednesday to help the police on the scene protect the building and the public. A handful of the F.B.I. agents arrived in camouflage and bearing shields and machine guns late in the afternoon outside the secure location where the senators were being held.

The deployment signaled the growing alarm among federal officials viewing the chaos swirling at the Capitol building on Wednesday.

“The F.B.I. has been deployed to assist our U.S. Capitol Police partners, as requested, in protection of federal property and public safety,” the F.B.I. statement said.

The bureau would not say how many of its agents were deployed to the Capitol. But a former government official said that all F.B.I. agents in the region were alerted earlier on Wednesday that they could be called to downtown Washington.

A woman who was shot inside the Capitol building after it was overrun by a pro-Trump mob has died, Washington, D.C., police officials said on Wednesday.

The woman has not been identified and no information has been released about who may have shot her. Chief Robert J. Contee of the Metropolitan Police Department said earlier that she was a “civilian” and that his officers were leading the investigation.

The woman was pronounced dead at a local hospital, Dustin Sternbeck, a spokesman for the police department, said in an email. Mr. Sternbeck said he did not yet know who shot her or have any other details.

A video posted to Twitter earlier on Wednesday appeared to show a shooting in the Capitol.

The woman in the video seemed to climb onto a small ledge next to a doorway inside the building immediately before a single loud bang is heard. The woman, draped in a flag, fell to the ground at the top of a stairwell. A man with a helmet and a military-style rifle stood next to her after she fell, and shouts of “police” could be heard as a man in a suit approached the woman and crouched next to her.

President Trump on Wednesday evening openly condoned the violence unfolding at the other end of Pennsylvania Avenue after a mob of his supporters stormed the Capitol.

“These are the things and events that happen when a sacred landslide election victory is so unceremoniously & viciously stripped away from great patriots who have been badly & unfairly treated for so long,” Mr. Trump tweeted Wednesday evening, after spending much of the afternoon in the Oval Office watching footage of escalating violence unfolding on Capitol Hill. “Go home with love & in peace. Remember this day forever!”

The tweet that appeared to prop up violent protesters as “patriots” and asserted baseless claims about the election outcome came after the president, under public and private pressure from advisers, had offered only a tepid response as the Capitol was breached for the first time in modern history and one woman died after being shot on the Capitol grounds.

Mr. Trump posted the message both on Twitter and his Facebook pages. Facebook removed the post. Twitter first attached a warning label to the tweet that said it made a disputed claim about election fraud before removing it all together, claiming it “violated the Twitter Rules.”

Even as former administration officials and Democratic leaders called on the president to tell the protesters to “go home,” Mr. Trump for hours did little to discourage them from storming the building. Instead, he issued two perfunctory tweets in which he asked them merely to remain “peaceful.”

“Remember, WE are the Party of Law & Order — respect the Law and our great men and women in Blue,” he wrote, after shocking scenes of broken windows and waving Confederate flags in the Capitol had been playing on television for hours.

The protesters had made their way to the Capitol at the president’s behest, after attending a rally near the White House, where he baselessly claimed the election results were fraudulent.

It was only hours into the melee, and after an explosive device was found at the Republican National Committee headquarters, that Mr. Trump released a message telling the mob to leave.

“You have to go home now,” he said in a video message filmed at the White House and posted on Twitter. “We have to have peace. We have to have law and order. We don’t want anyone hurt.” Still, the president ultimately offered encouragement to the mob, noting: “We love you. You’re very special,” and “I know how you feel.”

But many advisers around the president were worried that his message in the video was not forceful enough and that some of his supporters would interpret it as encouragement to continue fighting for him.

Alyssa Farah, who resigned last month from her post as the White House communications director, tweeted a more direct message at the president’s supporters.

“Dear MAGA- I am one of you. Before I worked for @realDonaldTrump, I worked for @MarkMeadows & @Jim_Jordan & the @freedomcaucus,” she said, establishing her conservative bona fides. “I marched in the 2010 Tea Party rallies. I campaigned w/ Trump & voted for him. But I need you to hear me: the Election was NOT stolen. We lost.”

Earlier in the day the president had also encouraged his supporters with an alternate message. “We will never concede,” Mr. Trump said at the rally.

At the Capitol, some lawmakers who were taken to secure locations blamed the president for the uprising. “This is what the president has caused today, this insurrection,” said Senator Mitt Romney, Republican of Utah.

Hours after the violence began, the White House press secretary, Kayleigh McEnany, said that the National Guard and other federal protective services were being deployed to the scene, at the president’s direction.

Some former administration officials publicly tried to encourage Mr. Trump to take a tougher stand to quell the escalating chaos, while other allies privately pressed him to do more. “The President’s tweet is not enough,” Mick Mulvaney, the former acting White House chief of staff, wrote on Twitter. “He can stop this now and needs to do exactly that. Tell these folks to go home.”

Ivanka Trump, the president’s daughter and a senior White House official, tweeted that “the violence must stop immediately,” first referring to them as “American patriots” before amending her statement online and condemning the violence outright.

In a joint statement, Senator Chuck Schumer and Speaker Nancy Pelosi, the Democratic leaders, said, “We are calling on President Trump to demand that all protesters leave the U.S. Capitol and Capitol grounds immediately.”

But Mr. Trump resisted those private and public entreaties to make any outright condemnation of the violence. Instead, his ire was more focused on Vice President Mike Pence, who earlier in the day made clear that he planned to reject the president’s pressure to block congressional certification of Mr. Biden’s victory. Mr. Pence was evacuated from the Senate chamber as the tension escalated.

“Mike Pence didn’t have the courage to do what should have been done to protect our Country and our Constitution, giving States a chance to certify a corrected set of facts, not the fraudulent or inaccurate ones which they were asked to previously certify. USA demands the truth!” Mr. Trump wrote on Twitter.

At the rally earlier on Wednesday, Mr. Trump insisted the country’s elections were worse than those in third-world nations, a statement that would be welcomed by authoritarians in countries that he has cozied up to throughout his four years in power.

He addressed the widely criticized call with Georgia’s secretary of state, Brad Raffensperger, which took place on Saturday and a recording of which was made public. In the call, the president urged Mr. Raffensperger to “find” additional votes to allow Mr. Trump to win the state. “People loved that conversation,” the president said.

At one point during the rally, Mr. Trump conceded that the two Republican candidates in the Georgia runoffs on Tuesday, Senator Kelly Loeffler and David Perdue, whose Senate term ended Sunday, had lost their races, saying they “didn’t have a shot” as he continued with baseless allegations of electoral fraud and theft.

At other points, he complained that he has no control over the three U.S. Supreme Court justices he appointed. And he complained about the former attorney general, William P. Barr, saying he had liked him, “but he changed, because he didn’t want to be considered my personal attorney.”

He also attacked Representative Liz Cheney, Republican of Wyoming and the party’s third-ranking House leader, who has criticized his efforts to undermine the election, saying she wanted to keep U.S. soldiers in other countries. “The Liz Cheneys of the world” need to be voted out, he said.

Talking about his inability to get his unvarnished statements into news circulation, Mr. Trump falsely declared, “That’s what happens in a communist country.”

Democrats took control of the Senate on Wednesday with a pair of historic victories in Georgia’s runoff elections, assuring slim majorities in both chambers of Congress for President-elect Joseph R. Biden Jr. and delivering an emphatic, final rebuke to President Trump in his last days in office.

The Rev. Raphael Warnock defeated Senator Kelly Loeffler, becoming the first Black Democrat elected to the Senate from the South. And Jon Ossoff, the 33-year-old head of a video production company who has never held public office, defeated David Perdue, who recently completed his first full term as senator.

Both Democrats now lead their defeated Republican opponents by margins that are larger than the threshold required to trigger a recount under Georgia law.

The Democrats’ twin victories will reshape the balance of power in Washington. Though they will have the thinnest of advantages in the House and Senate, where Vice President-elect Kamala Harris will break 50-50 ties, Democrats will control the committees and the legislation and nominations brought to the floor. That advantage will pave the way for at least some elements of Mr. Biden’s agenda.

Mr. Ossoff’s victory comes at a moment when the nation’s political leadership has been paralyzed by a pro-Trump mob that stormed the Capitol and halted the formal accepting of the Electoral College results by Congress. The day’s extraordinary proceedings — rioting interrupting the peaceful transition of political power — crystallized the campaign the Georgia Democrats ran against their Republican opponents, both of whom pledged to seek to overturn the results of the presidential election to keep Mr. Trump in office.

The Republicans’ losses in a state that Mr. Biden narrowly carried in November, but that still leans right politically, also amounted to a vivid illustration of the perils of embracing Mr. Trump. He put his diminished political capital on the line with an election eve appearance in Northwest Georgia. And Mr. Perdue and Ms. Loeffler unwaveringly embraced the president throughout the runoff races even as he refused to acknowledge Mr. Biden’s victory and brazenly demanded that Georgia state officials overturn his loss in the state.

The political fallout of Mr. Trump’s tenure is now clear: His single term in the White House will conclude with Republicans having lost the presidency, the House and the Senate on his watch.

Mr. Ossoff and Mr. Warnock won thanks to a frenetic get-out-the-vote push that began immediately after the November election, when no candidate in either race claimed the majority needed to avoid a runoff. Driving turnout among liberals and Black voters in the early-voting period, Democrats built an insurmountable advantage going into election day.

They won thanks to overwhelming margins in Georgia’s cities, decisive victories in Georgia’s once-Republican suburbs and because of lackluster turnout on Tuesday in the rural counties that now make up the G.O.P. base.

An explosive device was found at the headquarters of the Republican National Committee in Washington and the nearby headquarters of the Democratic National Committee was evacuated after the discovery of a suspicious package on Wednesday, according to three people briefed on the discoveries.

The device that was found at the R.N.C. was a pipe bomb that was successfully destroyed by a bomb squad, according to an official for the R.N.C.

The package at the D.N.C. has yet to be identified, according to a top Democrat briefed on the matter who was not authorized to speak publicly about it.

The R.N.C. and D.N.C. are headquartered just a few blocks away from the U.S. Capitol, which Mr. Trump’s supporters stormed on Wednesday afternoon soon as Congress had gathered to certify President-elect Joseph R. Biden Jr.’s victory and shortly after the president addressed the crowd near the White House.

As a mob breached the Capitol, Vice President Mike Pence was rushed from the Senate chamber and the building was placed on lockdown. Shortly after, Mr. Trump tweeted that Mr. Pence “didn’t have the courage to do what should have been done” because he did not try to reject the electors.

The National Guard for Washington and Virginia was activated Wednesday afternoon to respond to the unrest.

Images beamed around the world of Trump supporters storming and vandalizing the United States Capitol elicited alarm from the nation’s allies — and glee from its critics.

“This is not merely a US. national issue, but it shakes the world, at least all democracies,” said Peter Beyer, the German government’s coordinator for trans-Atlantic affairs.

In France, a member of the European Parliament, Nathalie Loiseau, sounded a warning that evoked the political battles in her own country. “A message to those who find populists amusing or are indifferent to them: This is what they are capable of,” she wrote on Twitter.

Later Wednesday evening, Secretary of State Mike Pompeo condemned the violence and said on Twitter that storming the Capitol was “unacceptable.”

Months after the Black Lives Matter protests put racial tensions and police bias in the United States into the international spotlight, some observers were quick to see the assault in Washington as a further breakdown of law enforcement.

Analysts on Mexican television pointed out that the members of the mob were overwhelmingly white, noting that the police response to Black or Latino protesters would likely have been more violent. Mexican reporters who have covered the United States closely watched in astonishment as their neighbor’s capital city descended into chaos.

“I’m amazed at the lack of preparedness of the Capitol police and D.C. police,” said Carlos Puig, a Mexican television host and newspaper columnist. “I guess the U.S. institutions never thought this would happen to them.”

In Russia, the violence fit neatly into the Kremlin’s propaganda narrative of a crumbling American democracy. Russia’s state-controlled news channel, Rossiya-24, broadcast the chaos at the Capitol as part of a split screen, with one side showing happy Orthodox Christmas festivities in Russia, the other the mayhem in Washington.

And in Israel, former Prime Minister Ehud Barak alluded to President Trump’s angry speechmaking in recent days as an open attempt at incitement.

“A shaky coup attempt on Capitol Hill. Lots of incitement by a defeated president who lost his temper,” Mr. Barak wrote on Twitter. “The lesson is clear: When those who are in charge are allowed to go wild, and those who had to act are paralyzed by fear — even the impossible can happen.”

— Melissa Eddy, Aurelien Breeden, Natalie Kitroeff, Oscar Lopez, Anton Troianovski, David M. Halbfinger, Isabel Kershner and Adam Rasgon

Vice President Mike Pence, in a bold statement on Wednesday afternoon, rejected President Trump’s pressure to block congressional certification of President-elect Joseph R. Biden Jr.’s victory in the presidential election, claiming that he lacked the “unilateral authority” to decide the outcome of the presidential election.

“As a student of history who loves the Constitution and reveres its Framers,” Mr. Pence wrote in a two-page letter, “I do not believe that the Founders of our country intended to invest the vice president with unilateral authority to decide which electoral votes should be counted during the Joint Session of Congress, and no vice president in American history has ever asserted such authority.”

The letter was released by the White House as Mr. Trump was speaking to a group of supporters at the Ellipse, where over and over he implored Mr. Pence to have “the courage to do what he has to do.”

Mr. Pence does not have the unilateral power to alter the results sent by the states to Congress.

But Mr. Trump, listening to the advice of allies like Rudolph W. Giuliani, his personal lawyer, has been convinced that the vice president could do his bidding. “If Mike Pence does the right thing, we win the election,” Mr. Trump said Wednesday, claiming inaccurately that the vice president has “the absolute right to” throw out the election results.

Mr. Pence’s defiance — the first in his four years as a deferential No. 2 — created a remarkable and uncomfortable split screen, as the president continued the public pressure campaign even as Mr. Pence arrived at the Capitol to preside over a joint session of Congress where the Electoral College vote will be certified.

On Tuesday night, after The New York Times reported that the vice president in a private meeting had informed Mr. Trump he did not have the authority to change the results of the election, Mr. Trump released a statement disputing the story. “He never said that,” the statement said. “The Vice President and I are in total agreement that the vice president has the power to act.”

The vice president’s advisers have been eager to find some middle ground where Mr. Pence could mollify Mr. Trump by acknowledging some of his concerns. In the letter, Mr. Pence indicated that he shared the president’s concerns about “integrity of this election” and would make sure that challenges received a “fair and open hearing” in Congress.

Releasing the letter ahead of his arrival at the Capitol took some of the drama and suspense out of Mr. Pence’s largely ceremonial role, and the swirling questions about how he would play the awkward moment. But his aides expected him to be on the receiving end of the president’s ire for not complying with his wishes. They expected him to underscore his loyalty to the Trump agenda in other ways, over the coming days.

On Wednesday, Kelli Ward, who chairs the Arizona Republican Party, also joined a group of far-right Republicans that petitioned the Supreme Court Justice Samuel Alito to grant Mr. Pence the authority to reject some state electors, after lower courts rejected the request. One of the attorneys who wrote the petition is Sidney Powell, a longtime member of Mr. Trump’s legal team.

On Wednesday afternoon, as Mr. Trump’s supporters left the rally and stormed the Capitol with rioters entering the building and Mr. Pence being quickly evacuated from a building that was on lockdown, the president did nothing to quell the disorder that he had encouraged earlier in the day. Instead, he focused his ire on the vice president.

“Mike Pence didn’t have the courage to do what should have been done to protect our Country and our Constitution, giving States a chance to certify a corrected set of facts, not the fraudulent or inaccurate ones which they were asked to previously certify. USA demands the truth!” he wrote on Twitter.

I’ve served 36 years in the Senate. This will be the most important vote I’ve ever cast. President Trump claims the election was stolen. The assertions range from specific local allegations to constitutional arguments to sweeping conspiracy theories. I supported the president’s right to use the legal system. Dozens of lawsuits received hearings in courtrooms all across our country, but over and over … … the courts rejected these claims, including all-star judges, whom the president himself has nominated. If this election were overturned by mere allegations from the losing side, our democracy would enter a death spiral. We’d never see the whole nation accept an election again. Every four years would be a scramble for power at any cost.

Senator Mitch McConnell of Kentucky, the most powerful Republican on Capitol Hill, forcefully rebuked President Trump and members of his own party on Wednesday as they sought to reject President-elect Joseph R. Biden Jr.’s victory, warning that the drive to overturn a legitimate election risked sending democracy into “a death spiral.”

In a lengthy speech defending his intention to vote against challenges to Mr. Biden’s victory — which he framed as “the most important vote I have ever cast” — Mr. McConnell urged his Republican colleagues ready to follow the president to step back from the brink.

He called some of Mr. Trump’s claims “sweeping conspiracy theories” and implicitly rebuked a dozen or so senators justifying their objections to the results by saying they were merely acts of protest.

“The voters, the courts and the states have all spoken,” Mr. McConnell, the majority leader, said. “If we overrule them all, it would damage our republic forever.”

He added a short time later: “If this election were overturned by mere allegations from the losing side, our democracy would enter a death spiral.”

But even as he spoke, there were signs outside the Capitol that the country was already in the throes of such a vicious cycle. Mr. McConnell, who was the first senator to rise in a debate over objections to electors from the state of Arizona, spoke as thousands of demonstrators massed outside the Capitol, clashing violently with the police and ultimately storming the building where Congress convenes.

Mr. McConnell’s remarks came on a day when he appeared to be headed back into the minority after six years of running the Senate, thanks, at least in part, to Mr. Trump’s relentless election attacks that have badly split the party. But while the president will be leaving office in two weeks, Mr. McConnell, 78, is likely to continue leading his party, and wants to play a crucial role in rebuilding it after years of Mr. Trump.

The intraparty brawl prompted by the election challenges was a situation Mr. McConnell had feared and that had prompted him to initially refrain from recognizing Mr. Biden’s victory for weeks after November’s election, wary of inflaming Mr. Trump’s grievances with his party.

When he did recognize Mr. Biden, his critics argued that the acknowledgment came too late, and that by waiting silently, Mr. McConnell had allowed Mr. Trump to sow dangerous disinformation with millions of Republican voters, drawing the backing of elected officials in his own party.

“It would be unfair and wrong to disenfranchise American voters and overrule the courts and the states on this thin basis,” he said. “I will vote to respect the people’s decision and defend our system of government as we know it.”

Facebook banned a page that was being used to organize pro-Trump demonstrations in Washington on Wednesday after direct calls for violence surfaced on the page.

The company said it removed the page, called Red-State Secession, on Wednesday morning. It did not provide any further details on what prompted the action.

In the days leading up to the protests in Washington, members of the group had asked its roughly 8,000 followers to share addresses of perceived “enemies” in the nation’s capital. Those included home addresses of federal judges, members of Congress and other prominent progressive politicians.

Comments left on the page often featured photos of gun and ammunition, along with emoji suggesting that members of the group were planning for violence. One post on Tuesday said people should be “prepared to use force to defend civilization.”

Several comments below the post showed photos of assault rifles, ammunition and other weapons. In the comments, people referred to “occupying” the capital and taking action to force Congress to overturn the election results.

Before it was removed by Facebook, the page directed followers to other social media sites like Gab and Parler that have gained popularity in right-wing circles since the election in November.

As supporters of President Trump breached the nation’s Capitol, hundreds of other Trump supporters across the country gathered at state capitols, in some cases prompting evacuations and law enforcement mobilizations, although none immediately appeared to turn violent.

In Georgia, law enforcement officers escorted Secretary of State Brad Raffensperger out of the State Capitol on Wednesday afternoon as a few dozen Trump supporters outside the building rallied to protest the recent election results.

Chris Hill, the leader of a right-wing militia, said he called some of his “troops” to the statehouse to protest, repeating the false claim that the election was “rigged.” Mr. Hill said he believes the nation is headed toward a civil war.

In New Mexico, a lawmaker reported that the State Police were evacuating the Capitol, while Denver’s mayor instructed city government buildings to close as about 700 people gathered outside the statehouse there. Authorities in Texas shut down the Capitol building “out of an abundance of caution.” In Washington State, protesters broke through the gates surrounding the governor’s mansion. A spokesman for Gov. Jay Inslee said he was in a safe location.

Trump supporters burned an effigy of Gov. Kate Brown of Oregon outside the Capitol there and later fought with counterprotesters. In Arizona, they set up a guillotine, while in Washington State, some gathered outside the Capitol with guns.

More than 500 people gathered in Lansing, Mich., praying and carrying a mix of flags and guns.

“We have a restored voice in Michigan,” said Rick Warzywak, one of the organizers of the rally from Atlanta, Mich. “No matter what happens today in D.C., do not be discouraged. We’re going to be in a consistent battle for weeks to come and we’re not going to give up.”

In Sacramento, Gov. Gavin Newsom of California canceled a news briefing on the coronavirus to ensure the safety of his staff, he said in a statement.

Some state capitol buildings have seen volatile demonstrations that have included clashes with the police and arrests in the weeks since the November election.

Vice President Mike Pence and other top Republican leaders denounced the violence on Capitol Hill on Wednesday, as President Trump’s efforts to encourage the mob of his supporters to leave peacefully drew criticism for not being forceful enough.

“This attack on our Capitol will not be tolerated and those involved will be prosecuted to the fullest extent of the law,” Mr. Pence wrote on Twitter. “The violence and destruction taking place at the US Capitol Must Stop and it Must Stop Now.”

Many of the other Republicans who sought to distance themselves from the mob violence on Wednesday had previously tolerated or outright encouraged efforts to subvert the results of the election.

Peaceful protest is the right of every American but this attack on our Capitol will not be tolerated and those involved will be prosecuted to the fullest extent of the law.

Senator Ted Cruz of Texas, the first Republican senator to object to the certification of election results during a joint session of Congress on Wednesday, denounced the storming of the Capitol building on Twitter, insisting that violence “is ALWAYS wrong.”

“Those storming the Capitol need to stop NOW,” Mr. Cruz wrote. “Those engaged in violence are hurting the cause they say they support.”

Representative Kevin McCarthy, the top Republican in the House and an early supporter of efforts to overturn the results of the election, called the violence on Capitol Hill “unacceptable” and “un-American.”

“I condemn any of this violence. I could not be more disappointed with the way our country looks right now,” Kevin McCarthy said in an appearance on Fox News, adding that he had called on the president to make a statement against the violence. “This is not the American way. This is not protected by the First Amendment. This must stop now.”

Senator Mitt Romney, Republican of Utah and an outspoken opponent of efforts by Republicans to subvert the election results, furiously denounced Mr. Trump for encouraging the chaos.

In a statement condemning the rioting hours later, Mr. Romney said that lawmakers should not be intimidated by the acts of violence, and he called on Congress to continue certification of the election results.

“We gather today due to a selfish man’s injured pride and the outrage of his supporters who he has deliberately misinformed,” Mr. Romney wrote. “We must not be intimidated or prevented from fulfilling our constitutional duty.”

Secretary of State Mike Pompeo and National Security Adviser Robert C. O’Brien, top members of Mr. Trump’s national security team, condemned the riots in statements released later in the evening.

“The storming of the U.S. Capitol today is unacceptable. Lawlessness and rioting — here or around the world — is always unacceptable,” Mr. Pompeo wrote.

Senator Marco Rubio, Republican of Florida, wrote on Twitter that there was “nothing patriotic about what is occurring on Capitol Hill.” He then pleaded with Mr. Trump to personally call for an end to the mob violence.

“Mr. President @realDonaldTrump the men & women of law enforcement are under assault,” Mr. Rubio wrote. “It is crucial you help restore order by sending resources to assist the police and ask those doing this to stand down.

Later in the evening, as law enforcement agencies evicted the mob from the building, Senator Ben Sasse, Republican of Nebraska, condemned the president for encouraging the violence, saying that “lies have consequences.”

“Today, the United States Capitol, — the world’s greatest symbol of self-government — was ransacked while the leader of the free world cowered behind his keyboard,” Mr. Sasse said in a statement. “This violence was the inevitable and ugly outcome of the president’s addiction to constantly stoking division.”

Senator Lindsey Graham, Republican of South Carolina and a longtime ally of President Trump, also denounced the storming of the Capitol building, demanding criminal prosecution for those who participated, and praised President-elect Joseph R. Biden Jr. for addressing the violence.

“I could not agree more with President-elect Biden’s statement to the nation. Time to retake the Capitol, end the violence, & stop the madness,” Mr. Graham said on Twitter. Republican members of the House who did not sign on to efforts to dispute the results of the election also vocally criticized the efforts.

“We are witnessing absolute banana republic crap in the United States Capitol right now.” Representative Mike Gallagher, Republican of Wisconsin, said in a video recorded in his congressional office, where he was sheltering in place. “This is the cost of countenancing an effort by Congress to overturn the election.”

Just days into his first term in Congress, Representative Peter Meijer, Republican of Michigan, denounced Mr. Trump after he posted a video in which he advised members of his mob to “go home” but also spoke in sympathetic and affectionate terms

“Enough. Acknowledge Biden as President-Elect and end this madness,” Mr. Meijer wrote on Twitter. “Violent rioters laid siege to the nation’s Capitol in an act of insurrection unparalleled in modern times. This is not leadership.”


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