WASHINGTON — The House moved on two fronts on Sunday to try to force President Trump from office, escalating pressure on the vice president to strip him of power and committing to quickly begin impeachment proceedings against him for inciting a mob that violently attacked the seat of American government.

In a letter to colleagues, Speaker Nancy Pelosi of California said the House would move forward on Monday with a resolution calling on Vice President Mike Pence and the cabinet to invoke the 25th Amendment, and wrest the powers of the presidency. She called on Mr. Pence to respond “within 24 hours” and indicated she expected a Tuesday vote on the resolution.

Next, she said, the House would bring an impeachment case to the floor. Though she did not specify how quickly it would move, leading Democrats have suggested they could press forward on a remarkably quick timetable, charging Mr. Trump by midweek with “high crimes and misdemeanors.”

“In protecting our Constitution and our democracy, we will act with urgency, because this president represents an imminent threat to both,” she wrote. “As the days go by, the horror of the ongoing assault on our democracy perpetrated by this president is intensified and so is the immediate need for action.”

Ms. Pelosi’s actions effectively gave Mr. Pence, who is said to be opposed to the idea, an ultimatum: use his power under the Constitution to force Mr. Trump out by declaring him unable to discharge his duties, or make him the first president in American history to be impeached twice.

Far from capitulating, Mr. Trump made plans to proceed as if the last five earth-shattering days had simply not happened at all. But momentum in Washington was shifting decisively against him.

More than 210 of the 222 Democrats in the House — nearly a majority — had already signed on to an impeachment resolution by Sunday afternoon, registering support for a measure that asserted that Mr. Trump would “remain a threat to national security, democracy, and the Constitution” if he was not removed in the final 10 days of his term. A second Republican senator, Patrick J. Toomey of Pennsylvania, said he should resign immediately, joining Lisa Murkowski of Alaska. And a Republican House member hinted more clearly than before that he could vote to impeach, even as he cautioned that it could backfire and further galvanize Mr. Trump’s supporters.

With few Democrats hopeful Mr. Pence would act, Representative James E. Clyburn of South Carolina, the party’s No. 3, said the House could vote to impeach Mr. Trump by Wednesday, one week before Inauguration Day. Lawmakers were put on notice to return to Washington, and their leaders consulted with the Federal Air Marshal Service and police on how to safely move them back into a Capitol that was ransacked in a shocking security failure less than a week ago.

“If we are the people’s house, let’s do the people’s work and let’s vote to impeach this president,” Mr. Clyburn said on “Fox News Sunday.” “The Senate will decide later what to do with that — an impeachment.”

Mr. Clyburn argued in favor of delaying the start of any Senate trial for several months to allow President-elect Joseph R. Biden Jr. to take office without the cloud of an all-consuming impeachment drama. It would be nearly impossible to start a trial before Jan. 20, and delaying it further would allow the House to deliver a stinging indictment of the president without impeding Mr. Biden’s ability to form a cabinet and confront the spiraling coronavirus crisis.

“Let’s give President-elect Biden the 100 days he needs to get his agenda off and running,” Mr. Clyburn, an influential ally of Mr. Biden, said in another interview on CNN.

The uncertainty underscored how little precedent those seeking to contain the president had to guide them. No president has been impeached in the final days of his term, or with the prospect of a trial after he leaves office — and certainly not just days after lawmakers themselves were attacked.

A two-thirds majority is needed to convict and remove a president in the Senate. But if he were found guilty, a simple majority of the Senate could then bar Mr. Trump from holding office in the future.

Mr. Biden has tried to keep a distance from the impeachment issue. He spoke privately Friday with Ms. Pelosi and Senator Chuck Schumer of New York, the top Senate Democrat. But publicly he has said that the decision rests with Congress, and that he intends to remain focused on the work of taking over the White House and the government’s coronavirus response.

“In 10 days, we move forward and rebuild — together,” Mr. Biden wrote on Twitter on Sunday.

At the White House, Mr. Trump remained out of sight for a fourth straight day and made no public comment on either the assault on the Capitol or the brewing impeachment threat. The White House announced instead that he would travel on Tuesday to Alamo, Texas, to promote his border wall as part of a series of activities highlighting what he sees as the achievements of the last four years.

Otherwise, the basic work of the final days of a presidential term had essentially been halted. A slew of pardons that were under discussion were put on hold after the riot, according to people informed about the deliberations. And around the White House, the president’s advisers hoped he would let go of giving himself a pardon, saying it would look terrible given what had taken place.

Among those said to be furious with the president was Melania Trump, the first lady. While she has stayed quiet publicly, people close to the situation said she was upset with her husband for what had taken place, as well as his decision not to attend Mr. Biden’s inauguration.

Other than a video message he posted on Thursday night, Mr. Trump has said nothing about the attack since its conclusion and taken no responsibility for it, nor has he said anything publicly about the U.S. Capitol Police officer killed by the mob. Only after much criticism did he order flags lowered to half-staff at the White House and other federal facilities on Sunday in honor of the officer and another who Capitol Police said had died off duty days after responding to the riot at the Capitol.

In past furors, any anger within his own party tended to fade with passing days, but this time, the disenchantment among many Republicans appeared to be hardening, particularly with new videos emerging, including one showing the mob dragging a police officer down the steps outside the Capitol and beating him.

“The more time, images, and stories removed from Wednesday the worse it gets,” Josh Holmes, a longtime adviser to Senator Mitch McConnell of Kentucky, the Republican leader, wrote on Twitter. “If you’re not in a white hot rage over what happened by now you’re not paying attention.”

It was that fury driving Democrats forward with stunning speed.

The four-page impeachment article that had gained overwhelming support among Democrats — written by Representatives David Cicilline of Rhode Island, Jamie Raskin of Maryland and Ted Lieu of California — was narrowly tailored to Mr. Trump’s role “willfully inciting violence against the government of the United States.” Democrats involved in the process said they had drafted the text with input from some Republicans, though they declined to name them.

None were expected to join as a co-sponsor before it was introduced on Monday, but Democrats said multiple House Republicans were privately discussing voting to impeach. When the House impeached Mr. Trump in 2019 for a pressure campaign on Ukraine to smear Mr. Biden, not a single Republican supported the charges.

“I’ll vote the right way, you know, if I’m presented with that,” said Representative Adam Kinzinger of Illinois.

The House indictment, which lawmakers and aides cautioned was still subject to change, would squarely blame for the rampage on Mr. Trump, stating that his encouragement was “consistent” with prior efforts to “subvert and obstruct” the election certification. That would include a Jan. 2 phone call pressuring Georgia’s secretary of state to “find” the votes he needed to claim victory in a state Mr. Biden clearly and legally won.

“It was an attack on our country and our democracy,” Mr. Cicilline said in an interview. “We simply cannot just allow this to stand unaddressed.”

More details emerged on Sunday about Mr. Trump’s role, which could shape the debate about impeachment. The president was deeply involved in the planning of the rally on Wednesday where he exhorted thousands of followers to march to the Capitol and demonstrate strength. He personally helped select who would speak and what music would play, according to people briefed on how the event came together.

The president had been excited about the event for days, more focused on that and trying to overturn the Electoral College vote count than anything else. Heading into Wednesday, some advisers privately said Mr. Trump appeared to believe that Mr. Pence could legally hand him the election in his role presiding over the vote count.

At one point, Mr. Trump told the vice president that he had spoken with Mark Martin, the former chief justice of the North Carolina Supreme Court, who he said had told him that Mr. Pence had that power. Mr. Pence had assured Mr. Trump that he did not. Mr. Trump made the vice president defend his rationale in a meeting with lawyers that Rudolph W. Giuliani had helped line up.

Both parties conceded they had no clear picture of how many senators in the party might ultimately vote to convict Mr. Trump.

Mr. Toomey said Mr. Trump had “spiraled down into a kind of madness” since the election and had effectively “disqualified himself” from ever running for office again. But a day after he called Mr. Trump’s conduct “impeachable,” Mr. Toomey argued an impeachment would be impractical with Mr. Trump already headed for the exit.

“I think the best way for our country, Chuck, is for the president to resign and go away as soon as possible,” he told the host Chuck Todd on NBC’s “Meet the Press.” “I acknowledge that may not be likely, but I think that would be best.”

In speaking with associates about the prospect of another impeachment, Mr. Trump was hit with the reality that few people from his defense team in last year’s Senate trial would be part of any new proceeding.

Jay Sekulow, who has served as his lead personal lawyer, and two other private lawyers, Marty Raskin and Jane Raskin, will not participate in a future impeachment defense, according to a person briefed on the planning, nor will Pat A. Cipollone, the White House counsel, or Patrick F. Philbin, his deputy.

This time, only a few of his allies on Capitol Hill have offered to speak up in defense as well. Among those who have, many have used calls for “unity” to argue against impeachment or calling for Mr. Trump’s resignation. In most cases, the lawmakers adamant that Democrats should let the country “move on” were among those who, even after Wednesday’s violence, voted to toss out electoral results in key swing states Mr. Biden won based on claims of widespread voter fraud that courts and the states themselves said were bogus.

“The Democrats are going to try to remove the president from office just seven days before he is set to leave anyway,” Representative Jim Jordan, Republican of Ohio, said on Fox News. “I do not see how that unifies the country.”

Michael D. Shear contributed reporting.