A person was shot and wounded Wednesday inside the US Capitol amid chaotic scenes in Washington as supporters of President Donald Trump entered the building in anger over his election defeat.

"One shooting victim was transported from the Capitol," a person attached to an emergency response unit told AFP, adding that there were "other injuries" in the chaotic protests and that the situation remained fluid.

The Washington Post reported that police said the victim was a white female shot in the shoulder, and CNN said she was in critical condition at a local hospital.

Protesters supporting Donald Trump swarmed the US Capitol, putting it on lockdown, as Vice President Mike Pence rebuffed the president's demand to overturn his loss to Democrat Joe Biden and the Senate's Republican leader denounced a bid in Congress to undo the election outcome.

Trump supporters overturned barricades and clashed with police on the US Capitol grounds and streamed inside the building. The demonstrations flared as lawmakers met inside to formally certify Biden's victory over Trump in the November 3 election. Law enforcement authorities struggled to maintain order.

The Senate and the House of Representatives, which were weighing objections to Biden's victory brought by a band of pro-Trump Republican lawmakers, abruptly and unexpectedly recessed.

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

Senate Majority Leader Mitch McConnell objected to the effort, saying, "If this election were overturned by mere allegations from the losing side, our democracy would enter a death spiral." McConnell 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 floor. "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 US 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.