Congress certified the election of President-elect Joseph R. Biden Jr. early Thursday, hours after loyalists urged on by President Trump stormed and occupied the Capitol, disrupting the final electoral count in a shocking display of violence that shook the core of American democracy.
Mr. Trump, who spent months stoking the anger of his supporters with false claims that the election was stolen and who refused to condemn the violent protests on Wednesday, said early Thursday that there would be an orderly presidential transition this month.
“Even though I totally disagree with the outcome of the election, and the facts bear me out, nevertheless there will be an orderly transition on January 20th,” he said in a statement.
The statement, which had to be issued through surrogates since Mr. Trump’s Twitter account was suspended, came moments after Vice President Mike Pence affirmed Mr. Biden as the winner of the presidential election shortly before 4 a.m. after the final electoral votes were tallied in a joint session of Congress.
There was no parallel in modern American history, with insurgents acting in the president’s name vandalizing Speaker Nancy Pelosi’s office, smashing windows, looting art and briefly taking control of the Senate chamber, where they took turns posing for photographs with fists up on the dais where Mr. Pence had just been presiding.
Mr. Biden, speaking as the scenes of destruction in the halls of Congress left lawmakers from both parties horrified, blamed Mr. Trump for fomenting the insurrection.
“At their best, the words of a president can inspire. At their worst, they can incite,” Mr. Biden said.
Allies around the world, accustomed to the chaos that has marked Mr. Trump’s tenure, struggled to find words to describe what they were witnessing.
“These pictures made me angry and sad,” Chancellor Angela Merkel of Germany said.
In Russia, by contrast, the violence fit neatly into the Kremlin’s narrative of a crumbling American democracy. The Kremlin released no official comment, but state television offered extensive late-night coverage of the attack on the Capitol, with the footage of the violence set to dramatic, orchestral music.
The upheaval unfolded on a day when Democrats secured a stunning pair of victories in runoff elections in Georgia, winning effective control of the Senate and the levers of power in Washington.
The siege at the Capitol was the climax of a weekslong campaign by Mr. Trump, filled with baseless claims of fraud and outright lies, to try to overturn a democratically decided election that he lost.
By the time the Senate reconvened late Wednesday, hours after lawmakers had been evacuated from a Capitol overrun by a mob carrying pro-Trump paraphernalia, one of the nation’s most polarizing moments had yielded an unexpected window of solidarity. Republicans and Democrats locked arms to denounce the violence and express their determination to carry out what they called a constitutionally sacrosanct function.
“To those who wreaked havoc in our Capitol today, you did not win,” Mr. Pence said in a sharp break from Mr. Trump, who had posted messages condoning the mob’s actions. “Violence never wins. Freedom wins. And this is still the people’s house.”
Senator Mitch McConnell, Republican of Kentucky and the majority leader, said the “failed insurrection” had only clarified Congress’s purpose.
“They tried to disrupt our democracy,” he said. “They failed.”
After the vote was certified early Thursday, Barry C. Black, the Senate chaplain, said a prayer in the chamber in an emotional close to a chaotic day in which a woman was fatally shot inside the Capitol.
“These tragedies have reminded us that words matter and that the power of life and death is in the tongue,” he said. “We deplore the desecration of the United States Capitol building, the shedding of innocent blood, the loss of life, and the quagmire of dysfunction that threaten our democracy.”
Congress rejected an attempt from Republicans to overturn the will of Pennsylvania voters early Thursday, effectively ending a final attempt from insurgents to turn a loss for President Trump in the state into a win.
The House rejected the challenge by a vote of 282 to 138, after a long debate dragged past 3 a.m. in Washington. A scuffle almost broke out on the chamber floor after Representative Conor Lamb, Democrat of Pennsylvania, delivered a particularly fiery speech in condemnation of the Republican objections.
“That attack today, it didn’t materialize out of nowhere,” Mr. Lamb said. “It was inspired by lies, the same lies you’re hearing in this room tonight, and the members who are repeating those lies should be ashamed of themselves.”
By a vote of 92 to 7, the Senate turned back the Pennsylvania challenge shortly before 1 a.m., as the number of objections to the counting of Electoral College votes dwindled after the mob’s brazen effort to keep President Trump in office, despite his decisive election loss in November.
Those senators voting against the results of the presidential election in Pennsylvania were: Josh Hawley of Missouri, Ted Cruz of Texas, Tommy Tuberville of Alabama, Cindy Hyde-Smith of Mississippi, Roger Marshall of Kansas, Cynthia Lummis of Wyoming and Rick Scott of Florida.
As most Republicans and all Democrats rejected the attempt, Senator Mike Lee, Republican of Utah, forcefully turned back the plot, registering his vote as “hell no.”
Earlier in the evening, lawmakers rejected an attempt to overturn the Arizona electoral slate. The House blocked the attempt with a 303-to-121 vote while the Senate offered a sharper rebuke with a 93-to-6 vote.
After debating the merits of subverting the majority of Arizona voters, lawmakers sped through the certification for several states after at least four Republican lawmakers, including Senator Kelly Loeffler of Georgia, said they had changed their minds and would vote to uphold the Electoral College results after having previously said that they would object to them.
Those voting against the results of the election in Arizona were: Mr. Hawley, Mr. Cruz, Mr. Tuberville, Ms. Hyde-Smith, Mr. Marshall and John Kennedy of Louisiana.
The move by Ms. Loeffler, who lost a special election in Georgia and failed to retain her Senate seat, amounted to one of her last acts in the upper chamber, and she announced her reversal during remarks on the Senate floor after the debate resumed late Wednesday.
Ms. Loeffler’s remarks came after Representative Cathy McMorris Rodgers of Washington and Senator Steve Daines of Montana condemned the actions of Trump loyalists who broke into the Capitol earlier on Wednesday and said they would no longer back an effort by some of their Republican colleagues to throw out the election results.
Ms. McMorris Rodgers’s remarks were particularly pointed.
“Thugs assaulted Capitol Police officers, breached and defaced our Capitol building, put people’s lives in danger and disregarded the values we hold dear as Americans,” Ms. McMorris Rodgers said in a statement, which she released a day after declaring she would object to the vote counts. “To anyone involved, shame on you.”
“What we have seen today is unlawful and unacceptable,” she added. “I have decided I will vote to uphold the Electoral College results, and I encourage Donald Trump to condemn and put an end to this madness.”
Shortly after Ms. McMorris Rodgers announced her decision, Mr. Daines followed suit, saying he, too, would certify electoral votes after having previously signed onto a letter saying he and other Republican senators “intend to vote on Jan. 6 to reject the electors” from some states.
“Today is a sad day for our country. The destruction and violence we saw at our Capitol today is an assault on our democracy, our Constitution and the rule of law, and must not be tolerated,” he said in his new statement Wednesday night.