President-elect Joe Biden on Thursday launched a blistering attack on Donald Trump after his supporters stormed the Capitol, saying the outgoing Republican leader was responsible for one of the "darkest days" in US history.

As the top two Democrats in Congress called for Trump's immediate removal from office, Transportation Secretary Elaine Chao became the first member of his cabinet to step down in protest at Wednesday's chaos.

Biden, at an event introducing his nominee for attorney general, declined to address the mounting demands for Trump's removal but accused him of unleashing an "all-out assault on the institutions of our democracy."

"Yesterday, in my view, was one of the darkest days in the history of our nation," the 78-year-old president-elect said.

"They weren't protesters," Biden said of the Trump supporters who attacked the Capitol while Congress was certifying the Democrat's November 3 election victory. "They were a riotous mob, insurrectionists, domestic terrorists."

"I wish we could say we couldn't see it coming but that isn't true," Biden said. "We could see it coming."

"The past four years, we've had a president who's made his contempt for our democracy, our Constitution, the rule of law clear in everything he has done," he said.

Biden's remarks came as House Speaker Nancy Pelosi and Senate minority leader Chuck Schumer, the two most powerful Democrats in Congress, called on Vice President Mike Pence to invoke the 25th Amendment, which allows a majority of the cabinet to replace a president deemed unable to discharge his duties.

"This is an emergency of the highest magnitude," Pelosi said, describing Trump as a "very dangerous person who should not continue in office."

"If the vice president and the cabinet do not act, the Congress may be prepared to move forward with impeachment," Pelosi said.

Schumer said Trump "should not hold office one day longer."

"What happened at the US Capitol yesterday was an insurrection against the United States, incited by the president," he said.

'End this nightmare'

Republican congressman Adam Kinzinger, a frequent Trump critic, said it was time to "end this nightmare" and also called for invoking the 25th Amendment, which has only been used before when a president has undergone a surgical procedure.

"The president is unfit," Kinzinger said. "And the president is unwell."

Invoking the amendment would make Pence president for the remaining two weeks the administration has in office.

Chao, who is married to Republican Senate Majority Leader Mitch McConnell and is one of Trump's longest-serving cabinet members, announced in a statement that she would resign as of Monday.

"Yesterday, our country experienced a traumatic and entirely avoidable event as supporters of the president stormed the Capitol building following a rally he addressed," Chao said.

"As I'm sure is the case with many of you, it has deeply troubled me in a way that I simply cannot set aside."

Mick Mulvaney, the US special envoy to Northern Ireland and a former Trump chief of staff, also announced he was resigning and said he expected others to step down.

"I can't stay here, not after yesterday," Mulvaney told CNBC television.

"And I wouldn't be surprised to see more of my friends resign over the course of the next 24 to 48 hours."

In an angry, rambling speech outside the White House before the violence, Trump urged his supporters to march to the Capitol and demanded that Pence, who ceremonially led the joint session of Congress, intervene to reverse their election defeat.

The vice president refused, and it was ultimately Pence standing who announced to lawmakers his and Trump's loss to Biden and incoming Vice President Kamala Harris.

Trump responded to Congress's late night certification of Biden's election win by pledging an "orderly transition" -- but once again refused to concede, repeating the unfounded allegations of election fraud that fueled the mob assault on Congress.

"Even though I totally disagree with the outcome of the election, and the facts bear me out, nevertheless there will be an orderly transition on January 20th," Trump said.

"While this represents the end of the greatest first term in presidential history, it's only the beginning of our fight to Make America Great Again!"

Trump released his statement through an aide's Twitter feed after being suspended by the social media platform -- a move also taken by Facebook.

Biden's pick for attorney general

The certification of Biden's November 3 election win came at the end of a marathon 15-hour joint session of the House of Representatives and Senate, which was interrupted for six hours by the mayhem at the Capitol.

Security forces fired tear gas to drive out the flag-waving crowds and police said a woman, reportedly a Trump supporter from southern California, was shot and killed.

The chaos at the Capitol came a day after Biden enjoyed a new triumph with Democrats projected to win two Senate seats in runoffs in Georgia -- handing the party full control of Congress and dramatically increasing Biden's ability to pass legislation and gain Senate confirmation of his nominees.

As the Justice Department and FBI vowed on Thursday to track down those involved, Biden announced that he was nominating Merrick Garland, a federal appeals court judge who was denied a seat on the Supreme Court by Republicans five years ago, to be his attorney general.