WASHINGTON — President Trump’s administration plunged deeper into crisis on Thursday as more officials resigned in protest, prominent Republicans broke with him and Democratic congressional leaders threatened to impeach him for encouraging a mob that stormed the Capitol a day earlier.

What was already shaping up as a volatile final stretch to the Trump presidency took on an air of national emergency as the White House emptied out and some Republicans joined Speaker Nancy Pelosi and a cascade of Democrats calling for Mr. Trump to be removed from office without waiting the 13 days until the inauguration of President-elect Joseph R. Biden Jr.

The prospect of actually short-circuiting Mr. Trump’s tenure in its last days appeared remote. Despite a rupture with Mr. Trump, Vice President Mike Pence privately ruled out invoking the disability clause of the 25th Amendment to sideline the president, as many had urged that he and the cabinet do, according to officials. Democrats suggested they could move quickly to impeachment, a step that would have its own logistical and political challenges.

But the highly charged debate about Mr. Trump’s capacity to govern even for less than two weeks underscored the depth of anger and anxiety after the invasion of the Capitol that forced lawmakers to evacuate, halted the counting of the Electoral College votes for several hours and left people dead, including a Capitol Hill police officer who died Thursday night.

Ending a day of public silence, Mr. Trump posted a 2½-minute video on Twitter on Thursday evening denouncing the mob attack in a way that he had refused to do a day earlier. Reading dutifully from a script prepared by his staff, he declared himself “outraged by the violence, lawlessness and mayhem” and told those who broke the law that “you will pay.”

While he did not give up his false claims of election fraud, he finally conceded defeat. “A new administration will be inaugurated on Jan. 20,” Mr. Trump acknowledged. “My focus now turns to ensuring a smooth, orderly and seamless transition of power. This moment calls for healing and reconciliation.”

Mr. Trump initially resisted taping the video, agreeing to do it only after aides pressed him and he appeared to suddenly realize he could face legal risk for prodding the mob, coming shortly after the chief federal prosecutor for Washington left open the possibility of investigating the president for illegally inciting the attack by telling supporters to march on the Capitol and show strength.

Pat A. Cipollone, the White House counsel, had warned Mr. Trump of just that danger on Wednesday as aides frantically tried to get the president to intervene and publicly call off rioters, which he did only belatedly, reluctantly and halfheartedly.

“We are looking at all actors, not only the people who went into the building,” Michael R. Sherwin, the U.S. attorney in Washington, told reporters. Asked if that included Mr. Trump, he did not rule it out. “We’re looking at all actors,” he repeated. “If the evidence fits the elements of a crime, they’re going to be charged.”

The president’s late, grudging video statement came after a day of disarray in the West Wing, where officials expressed growing alarm about the president’s erratic behavior and sought to keep more staff members from marching out the door. Aides hoped the latest statement would at least stanch the bleeding within Mr. Trump’s own party. Ivanka Trump, his eldest daughter, called lawmakers before it posted, promising it would reassure them.

Despite the talk of healing, however, Mr. Trump quietly made plans to take a trip next week to the southwestern border to highlight his hard-line immigration policies, which have inflamed Washington over the years, according to a person briefed on the planning. He also told advisers he wanted to give a media exit interview, which they presumed might undercut any conciliatory notes. But the first family has discussed leaving the White House for good on Jan. 19, the day before the inauguration.

Washington remained on edge on Thursday, awakening as if from a nightmare that turned out to be real and a changed political reality that caused many to reassess the future. As debris was swept up, businesses and storefronts remained boarded up, thousands of National Guard troops began fanning out around the city and some of the participants in the attack were arrested. Amid scrutiny over the security breakdown, the Capitol Police chief and the Senate sergeant-at-arms resigned.

The main focus, however, was on Mr. Trump. Ms. Pelosi and Senator Chuck Schumer of New York, the Democratic leader, called on Mr. Pence and the cabinet to invoke the 25th Amendment. But after the vice president refused to take their telephone calls, Ms. Pelosi told reporters that she would pursue impeachment if he did not act.

“While it’s only 13 days left, any day can be a horror show for America,” Ms. Pelosi said, calling Mr. Trump’s actions on Wednesday a “seditious act.”

“This president should not hold office one day longer,” said Mr. Schumer, who will become majority leader with the seating of two Democrats elected to the Senate in Georgia this week and the inauguration of Vice President-elect Kamala Harris as the tiebreaker.

Mr. Biden would not address whether Mr. Trump should remain in office but called Wednesday “one of the darkest days in the history of our nation” and forcefully laid blame at the president’s feet after years of stirring the pot. “I wish we could say we couldn’t see it coming,” he said. “But that isn’t true. We could see it coming.”

Even aides to Mr. Trump quietly discussed among themselves the possibility of invoking the 25th Amendment, and several prominent Republicans and Republican-leaning business groups endorsed the idea, including John F. Kelly, a former White House chief of staff to Mr. Trump; Representative Adam Kinzinger of Illinois; Gov. Larry Hogan of Maryland; and Michael Chertoff, a former homeland security secretary under President George W. Bush.

The conservative editorial page of The Wall Street Journal called on Mr. Trump to resign, terming his actions “impeachable.”

But Mr. Pence, several cabinet secretaries and other administration officials concluded that the 25th Amendment was an unwieldy mechanism to remove a president, according to people informed about the discussions. The notion became even less plausible when two cabinet members — Elaine L. Chao, the transportation secretary, and Betsy DeVos, the education secretary — resigned in protest of the president’s encouragement of the mob.

John R. Bolton, a former national security adviser to Mr. Trump who broke with him, said the idea was misguided. “People glibly have been saying it’s for situations like this,” he said in an interview. In fact, he said, the process of declaring a president unable to discharge his duties is drawn out and could lead to the chaos of having two people claiming to be president simultaneously.

While an impeachment conviction would only strip Mr. Trump of his power days earlier than he is set to lose it anyway, it could also disqualify him from running again in 2024. And even if another impeachment might not be any more successful than the first one, in which he was acquitted by the Senate last year in the Ukraine pressure scheme, advocates argued that the mere threat of it could serve as a deterrent for the remaining days of his tenure.

The latest danger signs may only encourage Mr. Trump to pardon himself before leaving office, an idea he had raised with aides even before the Capitol siege, according to two people with knowledge of the discussions.

In several conversations since Election Day, Mr. Trump has told advisers that he is considering giving himself a pardon and, in other instances, asked whether he should and what the effect would be on him legally and politically, according to the two people.

Mr. Trump has shown signs that his level of interest in pardoning himself goes beyond idle musings. He has long maintained he has the power to pardon himself, and his survey of aides’ views is typically a sign that he is preparing to follow through on his aims. He has also become increasingly convinced that his perceived enemies will use the levers of law enforcement to target him after he leaves office.

Despite ransacking the Capitol, the mob failed to stop Congress from counting the Electoral College votes in the final procedural stage of the election held Nov. 3. After the rioters were cleared from the building, lawmakers voted down efforts by Mr. Trump’s Republican allies to block electors from swing states and formally sealed Mr. Biden’s victory at 3:41 a.m. Thursday with Mr. Pence presiding in his role as president of the Senate.

Mr. Trump’s Twitter account was suspended for part of the day on Thursday before being restored, temporarily depriving him of that platform. But Facebook and Instagram barred him from their sites for the remainder of his presidency.

Behind the scenes, Mr. Trump railed about Mr. Pence, who refused to use his position presiding over the electoral count to block it despite the president’s repeated demands.

The vice president, who for four years had remained loyal to Mr. Trump to the point of obsequiousness, was angry in return at the president’s public lashing. Senator James M. Inhofe, Republican of Oklahoma, told The Tulsa World that Mr. Pence privately expressed a sense of betrayal by Mr. Trump “after all the things I’ve done for him.”

Even when the vice president had to be evacuated during the siege on Wednesday, the president never checked with him personally to make sure he was OK. The Secret Service agents wanted the vice president to leave the building, but he refused and sheltered in the basement, according to two officials. Congressional leaders were whisked to Fort McNair for their safety, but the vice president later urged them to finish the count at the Capitol.

On Thursday, Mr. Pence did not go to the White House complex, instead working out of the vice-presidential residence, according to administration officials.

He was not the only one feeling betrayed by the president. In the White House, aides were exasperated and despondent, convinced that Mr. Trump had effectively nullified four years of work and ensured that his presidency would be defined in history by the image of him sending a mob to the Capitol in an assault on democracy.

Ms. Chao stepped down a day after her husband, Senator Mitch McConnell of Kentucky, the Republican leader, forcefully repudiated Mr. Trump’s effort to overturn the election. “Yesterday, our country experienced a traumatic and entirely avoidable event as supporters of the president stormed the Capitol building following a rally he addressed,” she wrote in her resignation letter. “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.”

In her own letter, Ms. DeVos laid the responsibility for the mayhem directly at Mr. Trump’s feet. “There is no mistaking the impact your rhetoric had on the situation, and it is the inflection point for me,” she wrote, just a couple weeks after Mr. Trump pardoned four security contractors convicted of war crimes in Iraq committed while working for her brother, Erik Prince.

In addition to three White House aides who resigned on Wednesday, others stepping down included Matthew Pottinger, the deputy national security adviser; Tyler Goodspeed, the acting chairman of the White House Council of Economic Advisers; and Mick Mulvaney, the former acting White House chief of staff, who has been serving as a special envoy to Northern Ireland.

Also leaving were two other National Security Council aides as well as officials at the Justice and Commerce Departments. Gabriel Noronha, a Trump appointee who worked on Iran issues at the State Department official, was fired after tweeting that the president was “entirely unfit to remain in office.”

“The events of yesterday made my position no longer tenable,” Mr. Goodspeed said in a brief interview. On CNBC, Mr. Mulvaney said, “I can’t stay here, not after yesterday.”

Mr. Mulvaney went further, suggesting Mr. Trump had become increasingly unhinged in recent months. “Clearly he is not the same as he was eight months ago and certainly the people advising him are not the same as they were eight months ago and that leads to a dangerous sort of combination, as you saw yesterday,” he said.

Former Attorney General William P. Barr, perhaps the president’s most important defender until stepping down last month after a falling out, denounced Mr. Trump. In a statement to The Associated Press, Mr. Barr said that the president’s actions were a “betrayal of his office and supporters” and that “orchestrating a mob to pressure Congress is inexcusable.”

Even one of Mr. Trump’s lawyers in his bid to reverse the election results in Pennsylvania, Jerome M. Marcus, broke with him on Thursday, filing a motion withdrawing because “the client has used the lawyer’s services to perpetrate a crime and the client insists upon taking action that the lawyer considers repugnant and with which the lawyer has a fundamental disagreement.”

But concern about the exodus grew among some officials, who feared what Mr. Trump could do without anyone around him and worried about destabilizing the United States in a dangerous world. Secretary of State Mike Pompeo; Robert C. O’Brien, the national security adviser; and John Ratcliffe, the director of national intelligence, among others, were urged to stay. Mr. Cipollone received calls from senators and cabinet members urging him to remain.

“I understand the high emotions here,” former Secretary of State Condoleezza Rice said in an interview, “but I hope that the national security team will stay in place because it’s important to send a signal to our adversaries that the United States is prepared and functioning and they shouldn’t try to take advantage at this time.”

In the weeks since the election, Mr. Trump has shrunk his circle, shutting out those who told him to concede and favoring those telling him what he wanted to hear, that he was somehow cheated of the presidency. As supporters stormed into the Capitol on Wednesday, Mr. Trump was initially pleased, officials said, and disregarded aides pleading with him to intercede.

Unable to get through to him, Mark Meadows, his chief of staff, sought help from Ivanka Trump. Former Gov. Chris Christie of New Jersey, a longtime friend who has publicly criticized his efforts to invalidate the election results, tried to call Mr. Trump during the violence, but could not get through to him.

The video that Mr. Trump eventually released on Wednesday justified the anger of the rioters even as he told them it was time to go home. Rather than condemn their action, he embraced them. “We love you,” he said. “You’re very special.”

Mr. Christie said he believed that Mr. Trump deliberately encouraged the crowd to march on the Capitol as a way to put pressure on Mr. Pence to reject the election results during the congressional count.

“Unfortunately, I think what the president showed yesterday is he believes he’s more important than the system, bigger than the office,” Mr. Christie told the radio show host Brian Kilmeade. “And I think he’s going to learn that that was a very, very big miscalculation.”

Peter Baker reported from Washington, and Maggie Haberman from New York.