Leading Democrat Nancy Pelosi has branded Donald Trump "a very dangerous man" and called for him to be immediately removed from office.
The speaker of the House of Representatives said Vice President Mike Pence should invoke the 25th amendment of the US constitution, which allows the cabinet to strip a sitting president of his powers.
A similar call came from her Democratic colleague Chuck Schumer, who is set to become the Senate Majority leader later this month.
The president has 13 days remaining in office before Joe Biden takes over, but pressure is building on his Republican colleagues to take action to remove him before then.
Other lawmakers have sought to begin impeachment proceedings against Trump — a process which, if successful, would mean he could not run for president again.
Four people died on Wednesday after Trump supporters stormed the US Capitol in an attempt to overturn the results of the election that saw Biden win.
The White House press secretary Kayleigh McEnany said Donald Trump's administration was committed to an “orderly transition of power” and condemned the violence at the US Capitol as “appalling, reprehensible and antithetical to the American way.”
But there was direct no word from the president himself.
The vice president or senior members of the cabinet made no public appearances on Thursday afternoon either, although the Transportation Secretary Elaine Chao resigned in protest following the Capitol attack.
Pelosi told her press conference on Thursday that she would begin impeachment proceedings if the 25th amendment was not invoked.
“The president of the United States incited an armed insurrection against America," she said.
“My friends, we are in a very difficult place in our country as long as Donald Trump still sits in the White House.”
She said Trump could seek to do further harm, adding: “Any day can be a horror show for America.”
Chuck Schumer said he and Pelosi had telephoned the vice president to make the 25th amendment request, but that he did not take their call.
Pelosi also said she’s seeking the resignation of Capitol Police Chief Steven Sund following Wednesday's violence.
“I wish we could say we couldn't see it coming but that isn't true. We could see it coming. He unleashed an all-out assault on our institutions from of our democracy from the outset and yesterday was the culmination of that unrelenting attack.”