When Representative Liz Cheney asserted at the House Jan. 6 hearing on Thursday that Trump administration cabinet members weighed invoking the constitutional process to remove President Donald J. Trump from office after the attack on the Capitol by his supporters, she did not immediately provide details or evidence.

But as the federal government convulsed in the hours and days after the deadly riot, a range of cabinet officials weighed their options, and consulted one another about how to steady the administration and ensure a peaceful transition to a new presidency.

Mike Pompeo, the secretary of state at the time, and Steven Mnuchin, then the Treasury secretary, discussed the possibility of invoking the 25th Amendment, which would have required the vice president and the majority of the cabinet to agree that the president could no longer fulfill his duties to begin a complex process of removal from office.

Their discussion was reported by Jonathan Karl of ABC News in his book “Betrayal,” and described to The New York Times by a person briefed on the discussion. Mr. Pompeo has denied the exchange took place, and Mr. Mnuchin has declined to comment.

Betsy DeVos, Mr. Trump’s education secretary, told USA Today this week that she raised with Vice President Mike Pence whether the cabinet should consider the 25th Amendment. But Mr. Pence, she said, “made it very clear that he was not going to go in that direction.”

She decided to resign. So did Matt Pottinger, the deputy national security adviser.

Eugene Scalia, then the labor secretary, discussed with colleagues right after the attack the need to steady the administration, according to three people familiar with the conversations.

Mr. Scalia called an aide to Mr. Pence, they said, to say that he was uncomfortable with Mr. Trump having the level of power that he did and that there needed to be more involvement from the cabinet. Mr. Pence’s team did not want to make such a move.

Mr. Scalia also had a conversation with Mr. Pompeo, which Mr. Pompeo shared with multiple people, in which Mr. Scalia suggested that someone needed to tell the president to resign voluntarily or to do something else to restore confidence in the government and a peaceful transition of power.

Mr. Pompeo replied sarcastically by asking how Mr. Scalia imagined that conversation with Mr. Trump would go.

Mr. Scalia and Mr. Pompeo, through an aide, declined to comment.

The reference by Ms. Cheney, a Wyoming Republican and the vice chairwoman of the House Jan. 6 committee, to the 25th Amendment being under consideration by cabinet members was one of the most striking assertions in the panel’s two-hour hearing. In the first of six planned public hearings, the committee presented a detailed case against Mr. Trump and the rioters who stormed the Capitol and delayed the congressional certification of the Electoral College results.

The panel has signaled that it plans to use the discussions about the 25th Amendment to show not only the chaos that Mr. Trump set off by helping stoke the riot but how little confidence those around him had in his ability to be president.

“You will hear about members of the Trump cabinet discussing the possibility of invoking the 25th Amendment, and replacing the president of the United States,” Ms. Cheney said as she read her opening statement at the hearing. “Multiple members of President Trump’s own cabinet resigned immediately after Jan. 6.”

In addition to Ms. DeVos, the transportation secretary, Elaine Chao — the wife of Senator Mitch McConnell, the Republican leader — also resigned.

At the hearing on Thursday, Ms. Cheney also asserted that Republican lawmakers who had been involved in helping Mr. Trump overturn the election sought pardons from the White House in the final days of the administration. The committee plans to use the pardon requests as evidence of how those who helped Mr. Trump had a consciousness of guilt about what they had done.

Ms. Cheney did not provide any evidence to substantiate her assertion, and she named only one lawmaker, Representative Scott Perry, Republican of Pennsylvania, as a pardon seeker.

In an email, Jay Ostrich, a spokesman for Mr. Perry, called the assertion “a ludicrous and soulless lie.”

Ms. Cheney promised that she would reveal supporting evidence at upcoming hearings, and a person familiar with the committee’s investigation said the panel had received testimony about the pardon requests.

Mr. Perry coordinated a plan to try to replace the acting attorney general, who was resisting Mr. Trump’s attempts to investigate baseless election-fraud reports, with a more compliant official. Mr. Perry also endorsed the idea of encouraging Mr. Trump’s supporters to march on the Capitol on Jan. 6.

The committee’s next hearing is scheduled for Monday, where the panel plans to lay out how Mr. Trump and his allies stoked the “Big Lie” that the election had been stolen. Two more hearings are scheduled for next week — one on Wednesday about the attempt at the Justice Department to oust the acting attorney general, and another on Thursday about the pressure campaign on Mr. Pence to block or delay certification of the electoral vote count.

Three former Justice Department officials have agreed to testify at the Wednesday hearing, according to a letter sent to the committee on Friday.

The three witnesses — Jeffrey A. Rosen, who was the acting attorney general, Richard P. Donoghue, the acting deputy attorney general, and Steven A. Engel, the former head of the Office of Legal Counsel — all participated in a tense meeting just before the Jan. 6 attack, where Mr. Trump considered firing Mr. Rosen and installing a loyalist in his place.

Even before Jan. 6, government officials under Mr. Trump had discussed invoking the 25th Amendment.

In the spring of 2017, after Mr. Trump fired James B. Comey, the F.B.I. director, the deputy attorney general, Rod J. Rosenstein, rattled by Mr. Trump’s handling of the dismissal, raised the possibility of invoking the 25th Amendment in a meeting with senior Justice Department and F.B.I. officials.

The acting F.B.I. director, Andrew G. McCabe, had opened a counterintelligence investigation into Mr. Trump’s ties to Russia and was pressing Mr. Rosenstein to appoint a special counsel. Mr. Rosenstein agreed that Mr. Trump’s possible ties to Russia should be investigated but said that if an inquiry uncovered troubling evidence of Mr. Trump’s ties to Russia, the only remedy would be to invoke the 25th Amendment.

Mr. Rosenstein then said that he had done the math and believed there were at least six cabinet officials who would go along with invoking it, including Attorney General Jeff Sessions and Homeland Security Secretary John F. Kelly. Despite raising the possibility, the idea went nowhere and Mr. Rosenstein appointed Robert S. Mueller III to be the special counsel.

In the years that followed, there were several disclosures about others who had discussed the possibility of invoking the amendment. In 2019, a book by an anonymous administration official recounted that senior White House officials believed that Mr. Pence would go along with invoking the amendment to oust Mr. Trump. Mr. Pence denied that claim.

A veteran CBS News producer named Ira Rosen wrote in his 2021 book about his time working in the news business that Stephen K. Bannon, the White House chief strategist until August 2017, had spoken with him about the 25th Amendment.

And Mark T. Esper, Mr. Trump’s final Senate-confirmed defense secretary, wrote in his recent book, “A Sacred Oath,” about the aftermath of an incident when Mr. Trump delivered a diatribe against the military during a meeting with the Joint Chiefs of Staff in the second half of his term.

“Months later, one of the officers present told me in a phone call that he went home that evening deeply concerned about what he had seen in his commander in chief,” Mr. Esper recounted, without identifying the person in question.

“The next morning, he said in a very sober tone, he started reading up on the 25th Amendment and the role of the cabinet as a check on the president,” Mr. Esper said. “He wanted to understand ‘what the cabinet needed to consider’ and what the process was.”

Mr. Esper said that in his own view, Mr. Trump’s behavior never rose to the standard required for invoking the 25th Amendment. But that was before the postelection period, by which time Mr. Esper had been fired by Mr. Trump.

Two days after the Capitol riot, Speaker Nancy Pelosi spoke to Gen. Mark A. Milley, the chairman of the Joint Chiefs.

“This is bad, but who knows what he might do?” Ms. Pelosi said, according to the book “Peril,” by Bob Woodward and Robert Costa. “He’s crazy. You know he’s crazy. He’s been crazy for a long time. So don’t say you don’t know what his state of mind is.”

“Madam Speaker,” General Milley replied, “I agree with you on everything.”

Luke Broadwater and Katie Benner contributed reporting.