The push from some of Democratic Party's most liberal members emerged as chaos enveloped the nation's capital and came just two weeks before Trump will be forced to leave office anyway when President-elect Joe Biden is inaugurated.
It's extremely unlikely that Congress will muster enough support to remove the president from office using either method, or even come close to doing so, and it would require the support of Republicans. The White House did not immediately respond to a request for comment.
Democratic Reps. Ayanna Pressley of Massachusetts and Ilhan Omar of Minnesota said they supported impeachment.
"Donald J. Trump incited this violence and is directly responsible for this attempted coup," Pressley wrote on Twitter. "He must be impeached and removed from office immediately."
Omar wrote, "I am drawing up Articles of Impeachment. Donald J. Trump should be impeached by the House of Representatives & removed from office by the United States Senate."
"We can't allow him to remain in office, it's a matter of preserving our Republic and we need to fulfill our oath," she said.
It's not clear whether impeachment will gain support from most Democrats, and it's almost certain there isn't enough time to remove him that way. If Democrats impeached Trump after he left office and he were convicted in the Senate, he would not be permitted to hold office again.
House Speaker Nancy Pelosi, D-Calif., who was evacuated from the floor of the House earlier in the day as protesters stormed the Capitol, did not immediately return a request for comment.
Several other House Democrats are now pursuing another means to hasten the moment Trump is constitutionally mandated to leave office.
Democratic Reps. Ted Lieu of California and David Cicilline of Rhode Island were drafting a letter to Vice President Mike Pence on Wednesday to demand that he invoke the 25th Amendment to the Constitution in order to oust the president, NBC News reported.
Under that amendment, the vice president and a majority of the Cabinet can declare the president no longer able to hold office.
If the president contests the declaration, however, it takes two-thirds of the House and the Senate to override him and remove him, an even higher burden than impeachment, which takes a majority of the House and two-thirds of the Senate.
Pence's office did not immediately return a request for comment on the draft letter.
Another Democrat, Rep. Katherine Clark of Massachusetts, said in a statement that Trump "must be removed from office and prevented from further endangering our country and our people," but did not specify.
Some elected Republicans also called for Trump to be removed from office, though no GOP members of Congress did so. Gov. Phil Scott of Vermont, a Republican, wrote on Twitter that "The fabric of our democracy and the principles of our republic are under attack by the President."
"President Trump should resign or be removed from office by his Cabinet, or by the Congress," Scott wrote.
Trump was impeached by the House last year on charges that he abused his power by urging Ukrainian President Volodymyr Zelenskiy to open an investigation into Biden and his family. He was acquitted by the Senate.
Talk of invoking the 25th Amendment has appeared intermittently throughout the Trump presidency, including recently.
In October, Pelosi introduced legislation that would create a commission that would assess presidential fitness for office, as envisioned by the 25th Amendment, but insisted that it had nothing to do with Trump. The legislation did not make it into law.
Then-Deputy Attorney General Rod Rosenstein suggested recruiting Cabinet members to invoke the 25th Amendment as early as 2017, The New York Times has reported. Rosenstein called the reporting factually inaccurate.
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