Hours after an extraordinary rally by Trump seeking to overturn the election, a flag-waving mob broke down barricades outside the Capitol and swarmed inside, rampaging through offices and onto the usually solemn legislative floors.

At least one person was shot and wounded and others injured inside the Capitol, an emergency responder said, with lawmakers evacuated and handed gas masks as police fired tear gas.

One Trump supporter in jeans and a baseball cap was pictured propping a leg up on House Speaker Nancy Pelosi's desk, where a threatening note had been left, as throngs of others climbed onto risers set up for Biden's inauguration on Jan. 20, holding a banner that read: "We the people will bring DC to its knees/We have the power."

Biden called the violence an "insurrection" and demanded that Trump immediately goes on national television to urge his supporters to lift the siege of the Capitol.

"Our democracy's under unprecedented assault," Biden said in his home state of Delaware.

"The scenes of chaos at the Capitol do not reflect a true America," he added. 

"This is not dissent. It's disorder. It's chaos. It borders on sedition. And it must end now."

Trump soon afterward released a video on Twitter in which he called on his supporters to leave but stood by his unfounded claims of election fraud.

"We have to have peace. So go home. We love you - you're very special," he said.

Sonya Fitzgerald, a 43-year-old Trump supporter from Florida, said on the Capitol steps: "You'll hear about this in the history books."

The chaos at the Capitol came a day after Biden enjoyed a new triumph, with his Democratic Party projected to win two Senate runoff seats, handing them full control of Congress. 

For more than two centuries, the joint session of Congress has been a quiet, ceremonial event that formally certifies the election winner - but Trump urged members of his Republican Party to reject the outcome.

"The President of the United States is inciting a coup. We will not be intimidated. We will not be deterred," tweeted Democratic Representative Karen Bass.

Representative Val Demings likewise denounced the storming of the Capitol as evidence of "a coup in progress" - in words echoed by half a dozen lawmakers.

Representative Elaine Luria said she had to evacuate because of a report of a pipe bomb and said she believed she heard gunshots.

"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," she said.

US allies also voiced shock, with British Prime Minister Boris Johnson denouncing the "disgraceful scenes" and German Foreign Minister Heiko Maas urging Trump backers to "stop trampling on democracy."

Mayor Muriel Bowser imposed a nighttime curfew in Washington and sought help from neighboring areas, with Virginia sending its National Guard.

Biden is certain to become president, with Democrats already controlling the House of Representatives, but more than 140 Republican House members and a dozen Republican senators have sided with Trump in challenging the results even though no evidence of fraud has been proven in court.

Republican Senate leader Senator Mitch McConnell, closely aligned with Trump throughout his presidency, denounced the challenge in an impassioned address, noting that the results were not even close.

"The voters, the courts and the states have all spoken. If we overrule them, it will damage our republic forever," said McConnell, who is set to lose his position of majority leader after Democrats' Senate wins.

"If this election were overturned by mere allegations from the losing side, our democracy would enter a death spiral," said McConnell, who also accused Democrats of not accepting Trump's surprise 2016 victory.

Senator Chuck Schumer voiced alarm moments before protesters entered the Capitol, saying: "An element of the Republican Party believes their political viability hinges on the endorsement of an attempted coup."

But Senator Ted Cruz, a Republican, pushed against Biden's certification by saying that many Americans did not accept the election results and needed an investigation.

"I would urge to both sides perhaps a bit less certitude and a bit more recognition that we are gathered at a time when democracy is in crisis," Cruz said shortly before the violence.

Trump had urged his supporters to march to the Capitol in an angry, rambling speech outside the White House.

Trump warned "weak" Republicans not to certify Biden's victory and put direct pressure on Vice President Mike Pence, who ceremonially presided over the session.

"We will never give up. We will never concede," Trump told the cheering crowd, few wearing masks despite a spike in Covid-19 cases.

"I hope Mike has the courage to do what he has to do."

As Trump was still speaking and Congress opened the session, Pence - dutifully loyal to Trump for four years and quiet since the election - said he would not intervene.

Pence was rushed out of the Capitol and in a statement urged Trump's supporters - some of whom have begun chanting against him - to "stop now."