WASHINGTON (Reuters) -In a dramatic day in the U.S. Congress, Vice President Mike Pence on Wednesday rejected Donald Trump's demand that he try to overturn the results of the presidential election and the Senate's top Republican denounced a bid by the president's allies to challenge Trump's loss to Democrat Joe Biden.

Pence, a loyal lieutenant during the four years of Trump's tumultuous presidency, presided over the opening of a joint session of Congress to formally certify Biden's Nov. 3 victory over Trump. A band of Republican lawmakers quickly challenged the results, first from the election battleground state of Arizona won by Biden.

The U.S. Capitol was put on lockdown as pro-Trump demonstrators swarmed outside the building as lawmakers met. Protesters breached security barricades around the building.

"If this election were overturned by mere allegations from the losing side, our democracy would enter a death spiral," Senate Majority Leader Mitch McConnell, who helped give Trump some of the biggest accomplishments of his presidency, including deep tax cuts and confirmation of conservative judicial nominees.

Biden won the election by 306-232 in the state-by-state Electoral College and by more than 7 million ballots in the national popular vote, but Trump continues to falsely claim there was widespread fraud and that he was the victor.

The voters, courts and states "have all spoken," McConnell said on the Senate. "If we overrule them, it would damage our republic forever," he added.

Senate Democratic Leader Chuck Schumer called the challenges "an attempted coup" and said, "The Congress does not determine the outcome of an election. The people do."

Pence turned away Trump's demand that the vice president unilaterally reject state electoral votes on the same day Trump's fellow Republicans were poised to lose their majority in the Senate. The joint session of Congress could last past midnight.

"We will never give up," Trump earlier told thousands of cheering supporters on a grassy expanse near the White House called the Ellipse. "We will never concede. It doesn't happen. You don't concede when there's theft involved."

Trump in his speech applied fresh pressure on Pence to try to reverse the election results. In a statement, Pence said he shares the concerns about the "integrity" of the election but that is not correct that he should be able to accept or reject electoral votes unilaterally.

The U.S. Constitution does not give Pence the power to unilaterally overturn the results of the election, but he is under pressure to do so from Trump.

"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 said in the statement.

The Electoral College results were presented alphabetically, starting with Alabama. Republicans raised their first objection to results from Arizona, with possible objections to follow for Georgia, Michigan, Nevada, Pennsylvania and Wisconsin.

Republican lawmakers cheered and Democrats groaned when the Arizona objection was brought.

State and federal reviews have debunked Trump's claims of widespread election fraud even as increasingly desperate legal efforts by his campaign and allies on the right to overturn the election have failed in numerous courts all the way up to the U.S. Supreme Court.

Biden is due to take office on Jan. 20.

In his speech to supporters, Trump praised the Republican lawmakers seeking to challenge the election as "brave" and called members of his party who oppose the effort "weak" and pathetic."

Pence presided over the start of proceedings in the Capitol.

"Mike Pence, I hope you're going to stand up for the good of our Constitution and the good of our country. And if you're not, I'm going to be very disappointed in you," Trump said in remarks that continued even as Pence rejected his request.

Senator Ted Cruz, seen as a potential 2024 presidential candidate, on Wednesday led at least 11 other Republican senators, alongside a majority of the 211 Republicans in the House, in objecting to Electoral College results being formally approved by Congress.

DRAMA IN CONGRESS

The House chamber was filled with Republicans, all in masks, on the right, despite social distancing guidelines. On the left side, Democrats were scattered. As Speaker Nancy Pelosi issued instructions about the start of the session, there were repeated shouts from the Republican side, interrupting her to object to social distancing rules.

Democrats won one U.S. Senate race in Georgia and led in another on Wednesday after a pair of runoff elections on Tuesday. Winning both races would give Democrats control of both chambers of Congress and the power to advance Biden's legislative agenda.

Cruz bucked Senate Majority Leader McConnell, who has recognized Biden's victory and urged his fellow Republicans not to pursue the challenges, which appear to lack the political support they would need to succeed. The Republican maneuvering has created fissures within Trump's party and among outside groups normally supportive of it.

Republican senators, including Josh Hawley and James Lankford, have joined forces with Cruz, while other prominent members of the party, including Senator Mitt Romney and Representative Liz Cheney, oppose it.

Thousands of Trump supporters, including some members of violent far-right groups, staged demonstrations as they took up the president's unfounded claim that the election was stolen from him in an elaborate conspiracy. Many donned Trump's trademark red "Make America Great Again" hats and flags bearing his name, and a few carried a large Christian cross.

Two of the president's sons, Donald Trump Jr. and Eric Trump, and his personal lawyer, Rudy Giuliani, also addressed the rally.

Some protesters clashed with police overnight. Police this week arrested the leader of the Proud Boys, a group that has supported Trump, on charges of destruction of property related to an earlier protest and possession of a firearms magazine.

Many Republican senators who have refused to challenge the election results have received death threats on their office voice mail, a senior Senate Republican aide said.

If the challenges are ultimately defeated as anticipated, Pence, acting in his role as president of the Senate, is expected to proclaim Biden the next president and Senator Kamala Harris as the next vice president.

When at least one House member and one Senate member objects to a state result, each chamber will hold separate debates for each of those states lasting up to two hours. Each chamber will then vote to accept or reject the challenge and then report the result to the joint session of Congress, before moving on to the next challenge.

(Reporting by Richard Cowan and Susan Cornwell; Additional reporting by Jonathan Landay; Writing by Will Dunham; Editing by Scott Malone, Sonya Hepinstall and Jonathan Oatis)