Washington D.C. - Outgoing president Donald Trump said he was "outraged by the violence, lawlessness and mayhem" after a group of his supporters stormed the Capitol and forced a halt to a Congressional joint sitting.

The statement came as calls for his ouster grew on Thursday and members of his administration quit in the wake of a tumultuous 24 hours in Washington that also saw lawmakers finally confirm incoming president Joe Biden's election victory.

Trump did not acknowledge his role in riling up his supporters with baseless allegations of election fraud and encouraging them to march to the Capitol.

He promised a smooth transition to President-elect Joe Biden (78), who defeated him in November's presidential election.

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However, in a message to his "wonderful supporters," Trump (74) added "I know you are disappointed but I also want you to know that our incredible journey is only just beginning."

The Democratic leaders in Congress, Nancy Pelosi and Chuck Schumer, demanded that Vice President Mike Pence remove Trump under the Constitution's 25th Amendment. The calls were echoed by a Republican governor, a Republican lawmaker and numerous House Democrats.

"If the vice president and Cabinet do not act, the Congress may be prepared to move forward with impeachment," Pelosi told a press conference. Trump was impeached in 2019, but the Senate cleared him of charges last year.

US Transportation Secretary Elaine Chao became the first Cabinet official to announce their resignation following the attack on the US Capitol. Chao, who is the wife of Senate Republican leader Mitch McConnell, said the "traumatic and entirely avoidable event" had "deeply troubled" her.

Another cabinet member, Education Secretary Betsy DeVos, also submitted her resignation, according to the New York Times.

Deputy national security adviser Matt Pottinger quit following the resignations of multiple administration officials.

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Meanwhile, Facebook banned Trump from his accounts indefinitely, citing his intent to "undermine the peaceful and lawful transition of power."

Twitter had locked Trump's account on Wednesday, though he was able to post from it nearly 24 hours later to post his Thursday video statement.

The joint session of Congress on Wednesday was abruptly halted after rioters breached both chambers of the Capitol building, forcing lawmakers to flee and hunker down until the siege ended.

One woman was shot and killed by Capitol police during the assault, the force said in a statement. Authorities said three others died in separate medical emergencies.

A police officer who was injured while responding to the riot died on Thursday night, Capitol police said.

Police said they had arrested 68 people so far, and US Acting Attorney General Jeffrey Rosen said authorities would make more arrests in the coming days.

The Justice Department would ensure that "those responsible for this attack on our government and the rule of law face the full consequences of their actions under the law," he added.

The US Attorney's office, in conjunction with the Justice Department's counter-terrorism division, had so far charged 40 cases, officials said.

The majority of those deal with unlawful entry on the Capitol grounds, while a small handful are assault cases. Eight of the cases were also firearm cases.

Fifteen federal cases will also be filed later in the day on Thursday. One man was arrested by federal agents with a military semi-automatic rifle and 11 Molotov cocktails, according to officials at the Department of Justice.

A 2-metre-tall fence was being erected around the US Capitol on Thursday and will stay in place for the next 30 days, including for Biden's inauguration on January 20. More National Guard troops from other states were being deployed to Washington.

The FBI was seeking tips on identifying rioters.

Amid criticism about how security failures allowed the mob to swarm the building, House Speaker Pelosi said she was seeking the resignation of Capitol police chief Steven Sund.

Sund defended his force, which is dedicated to protecting the Capitol grounds, saying officers' response was "heroic" in the face of "criminal riotous behaviour." They were attacked by the rioters with metal pipes and chemical irritants, he said.

US media reported Sund will resign amid criticism. The resignation will be effective January 16, according to outlets including CNN and NBC, both citing police officials.

After the House and Senate reconvened, McConnell condemned the ransacking of the Capitol as a "failed insurrection."

Although several Republican senators who had planned to raise objections to the counting of votes in states won by Biden changed course after the attack, two challenges were still put forward. The moves caused lengthy delays to the certification process, but both challenges were ultimately rejected.

Longtime Trump loyalists including McConnell and Pence rebuffed the president's demands to block the certification of the election.

The violence around Congress was criticized by leaders around the world.