The House and Senate began a lengthy debate over President-elect Joe Biden’s victory as Republicans lodged their first objection to accepting the election results. President Trump addressed supporters near the White House before protesters marched to Capitol Hill.

Chaos engulfed the Capitol on Wednesday as a faction of Republicans sought to overturn President-elect Joseph R. Biden Jr.’s victory in Congress and a group of protesters loyal to President Trump tried to storm the building, demanding to be heard.

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

A group of Republicans led by Senator Ted Cruz of Texas objected early Wednesday afternoon to the counting of Arizona’s electoral votes, lodging the first of several extraordinary challenges to its outcome and forcing a two-hour debate in the House and Senate over Mr. Trump’s reckless election fraud claims.

“I rise for myself and 60 of my colleges to object to the count of the electoral ballots from Arizona,” said Representative Paul Gosar, Republican of Arizona. His objection was met with widespread applause by Republicans gathered on the floor of the House of Representatives for the joint session.

Bipartisan majorities in each chamber were prepared to turn back that challenge and others and formalize Mr. Biden’s victory. But the marathon session promised to be a volatile final act of the Trump presidency, with Mr. Trump — unwilling to cede the limelight or his fantasy of victory — transforming a moment of Democratic triumph into a day of defiance by summoning supporters to his backyard for an airing of grievances.

“We will never give up. We will never concede. It doesn’t happen,” Mr. Trump told a gathering of die-hard fans at the Ellipse behind the White House. He urged them to go to the Capitol to register their discontent, not long before a group of protesters breached barricades outside the edifice, clashing with police.

By using the proceeding as a forum for trying to subvert a democratic election, Mr. Trump and his allies are going where no party has since the Reconstruction era of the 19th century when Congress bargained over the presidency. The effort had already badly divided the Republican Party, forcing lawmakers to go on the record either siding with the president or upholding the results of a democratic election.

The objection to Arizona was the first of at least three expected during Wednesday’s session. Republicans were also eyeing Georgia and Pennsylvania, battleground states Mr. Biden won, for likely objections.

Lawmakers anticipated possible objections for up to three additional states — Michigan, Nevada, and Wisconsin — although it was not clear whether they would draw the requisite backing from a member of both the House and the Senate to be considered.

Mr. Cruz, a possible 2024 presidential contender, and his allies in the Senate has said he is merely trying to draw attention to the need for an electoral commission to audit the results. But by objecting, he joined ranks with a group of dozens of House Republicans backing Mr. Trump’s attempt to toss out the will of the voters to deliver him a second term in office.

Even before it began, the session was already driving sharp wedges into the Republican Party that threatened to do lasting damage to its cohesion, as lawmakers decided to cast their lot with Mr. Trump or the Constitution. Top party leaders in the House and Senate appeared to be headed for a high-profile split. And while only a dozen or so senators were expected to vote to reject the outcome in key states, as many as 70 percent of House Republicans could join the effort, stoking the dangerous belief of tens of millions of voters that Mr. Biden was elected illegitimately.

Despite a remarkable pressure campaign by Mr. Trump to unilaterally throw out states that supported Mr. Biden, Vice President Mike Pence, who was presiding as the president of the Senate, said just before the session began that he did not believe doing so was constitutional and would exercise his duties as his predecessors had. The outcome, after four years of loyal support for the president, risked his political standing in a party Mr. Trump still dominates.

“It is my considered judgment that my oath to support and defend the Constitution constrains me from claiming unilateral authority to determine which electoral votes should be counted and which should not,” he wrote in a letter.

Congress’s counting process began at 1 p.m. and the session had already accepted results from Alabama and Alaska before the objection to Arizona was lodged. A member of the House and Senate must agree for any objection to having force.

The House and Senate are convening Wednesday for a joint session of Congress to tally electoral votes from all 50 states and the District of Columbia, the final step in confirming President-elect Joe Biden’s victory in the presidential election over challenges from Republicans that will lengthen the proceedings.

Required under the Constitution, the meeting is typically a ceremonial affair, marking the final step in the electoral process before the presidential inauguration on January 20. But this year’s session is far from routine, as a coalition of Republicans from both chambers will try to reject some states’ election results over alleged election irregularities, while outside the halls of Congress, President Trump’s supporters have descended on the nation’s capital to make their final push to keep him in office.

Soon after the joint session began, GOP lawmakers objected to results from Arizona, a move that prompts two hours of debate in each chamber. A majority of each chamber would be required to reject Arizona’s electors, a virtual impossibility has given Democrats’ control of the House. More lawmakers have promised to contest the results in Pennsylvania and other battleground states.

In an extraordinary rebuke just before the joint session convened, Vice President Mike Pence defied the president and told lawmakers he does not have the authority to reject states’ electoral votes. Mr. Trump has repeatedly pressured Pence to reject votes from several states, a power the vice president does not have under the Constitution.

The plan from some GOP lawmakers to challenge the electoral votes split Senate Republicans, with more than a dozen committing to counting the results.

The joint sessions to tally the results of the 2012 and 2016 elections each lasted less than an hour. But Wednesday’s event is expected to stretch into the evening because of the Republican attempts to toss the electoral votes from some battleground states.

Under the Constitution, the final step in the 2020 presidential election is for a joint session of Congress to meet on Jan. 6 to count the Electoral College votes and officially declare a winner. Governors certified and sealed their states’ results after their electors signed off on them on Dec. 14, and Joe Biden and Kamala Harris won with 306 votes to Donald Trump and Mike Pence’s 232 votes.

This session is typically a ceremonial affair, but this year it’s expected to highlight the bitterly divided reaction between the two parties to the 2020 election results and last for hours.

Some of those members even acknowledged that they don’t expect to succeed or change the outcome, but are using the process to highlight what they believe are instances of fraud. None have provided any evidence to date, and legal challenges in states mounted by the Trump campaign and its allies have consistently failed.

How the joint session will work

Vice President Pence presides over the joint session, and it is his duty under the law to announce the results. Members of the House and Senate will convene in the House chamber at 1 p.m. ET.

The certificates from each state are opened and read in alphabetical order. If any House member raises an objection, they need a senator to sign the objection in order for it to be considered. According to GOP sources familiar with the discussions about the plans, the Republican lawmakers planning to object on Wednesday are focused primarily on three states — Arizona, Georgia, and Pennsylvania. They are also weighing challenges for Michigan, Nevada, and Wisconsin.

Texas GOP Sen. Ted Cruz is expected to sign onto the challenge regarding Arizona’s results and press for the appointment of an electoral commission that can examine any claims related to voter fraud.

Process for considering and voting on an objection

If both a House member and senator register their objection in writing, the joint session is recessed, and the House and Senate meet separately to debate the issue for up to two hours. Members are allowed up to 5 minutes each to speak and then both chambers vote. A simple majority is needed in both chambers for an objection to succeed.

With social distancing rules during the coronavirus pandemic, voting takes longer, so each objection could result in multiple hours of debate and vote timing.

House Speaker Nancy Pelosi, D-Calif., will preside over any House debate and has tapped Democratic Reps. Adam Schiff, Calif., Zoe Lofgren, Calif., Jamie Raskin, Md., and Joe Neguse, Colo., to lead any responses to GOP objections. But other Democrats from states Republicans are focused on are expected to also speak out against the effort as well.

In a letter to House Democrats on Monday evening, Pelosi called the day one “of historic significance” and says Biden and Harris won “decisively.” She cautioned that members should view the session as “a solemn occasion” and “we will have a civics lesson about protecting the integrity of our democracy.”

Pence, as president of the Senate, is expected to preside over the Senate debate. But Iowa GOP Sen. Chuck Grassley, who is president pro tem, is prepared to also be available if Pence is not available for any portion of the debate. The president falsely claimed the vice president could alter the results, but neither the Constitution nor any federal law allows for that.

After the New York Times reported Tuesday that Pence told the president at a lunch at the White House that he does not have the ability to block the certification for Biden, Trump released a statement late in the evening calling that report “fake news.”

The statement from the president maintains: “The Vice President and I are in total agreement that the Vice President has the power to act” and the vice president has “several options under the U.S. Constitution.”

After each chamber votes — and no challenge is expected to garner enough to succeed — the members of House and Senate return to the joint session and move onto the next state. After they have processed all the results, Pence reads the final tally and announces the election results for the president and vice president.

Leaders have warned members the process is likely to last several hours and could involve late-night votes. Democrats hold the majority in the House and roughly two dozen Republicans in the Senate, including Senate Majority Leader Mitch McConnell, R-Ky., have indicated they will join Democrats to certify Biden as the winner, so the outcome is not in doubt.

Thousands of pro-Trump protesters are expected to descend on Washington to voice support for the GOP objections. D.C. Mayor Muriel Bowser has advised residents to stay away from downtown and local law enforcement is prepared to respond to any possible violent demonstrations.