WASHINGTON — In the days before the Jan. 6 attack on the Capitol, some of President Donald J. Trump’s most extreme allies and members of right-wing militia groups urged him to use his power as commander in chief to unleash the military to help keep him in office.

Now, as the House committee investigating last year’s riot uncovers new evidence about the lengths to which Mr. Trump was willing to go to cling to power, some lawmakers on the panel have quietly begun discussions about rewriting the Insurrection Act, the 1807 law that gives presidents wide authority to deploy the military within the United States to respond to a rebellion.

The discussions are preliminary, and debate over the act has been fraught in the aftermath of Mr. Trump’s presidency. Proponents envision a doomsday scenario in which a rogue future president might try to use the military to stoke — rather than put down — an insurrection, or to abuse protesters. But skeptics worry about depriving a president of the power to quickly deploy armed troops in the event of an uprising, as presidents did during the Civil War and the civil rights era.

While Mr. Trump never invoked the law, he threatened to do so in 2020 to have the military crack down on crowds protesting the police killing of George Floyd. Stephen Miller, one of his top advisers, also proposed putting it into effect to turn back migrants at the southwestern border, an idea that was rejected by the defense secretary at the time, Mark T. Esper.

And as Mr. Trump grasped for ways to overturn his defeat in the 2020 presidential election, some hard-right advisers encouraged him to declare martial law and deploy U.S. troops to seize voting machines. In the run-up to the Jan. 6 attack, members of right-wing militia groups also encouraged Mr. Trump to invoke the law, believing that he was on the brink of giving them approval to descend on Washington with weapons to fight on his behalf.

“There are many of us who are of the view that the Insurrection Act, which the former president threatened to invoke multiple times throughout 2020, bears a review,” said Representative Zoe Lofgren, Democrat of California and a member of the Jan. 6 committee.

While no evidence has emerged that Mr. Trump planned to invoke the act to stay in office, people close to him were pushing for him to do so. Michael T. Flynn, Mr. Trump’s first national security adviser, attended a meeting in the Oval Office on Dec. 18, 2020, in which participants discussed seizing voting machines, declaring a national emergency and invoking certain national security emergency powers. That meeting came after Mr. Flynn gave an interview to the right-wing television network Newsmax in which he talked about a purported precedent for deploying troops and declaring martial law to “rerun” the election.

The idea was also floated by Roger J. Stone Jr., the political operative and longtime confidant of Mr. Trump, who told the conspiracy theorist Alex Jones in an interview that Mr. Trump should consider invoking the Insurrection Act.

In the weeks before the riot, the notion was prevalent among militia members and other hard-right supporters of Mr. Trump. It has surfaced repeatedly in evidence that federal prosectors and the House committee have obtained during their investigations into the Capitol attack.

In December 2020, Stewart Rhodes, the leader of the Oath Keepers militia group, wrote an open letter to Mr. Trump in which he called on the president to “use the Insurrection Act to ‘stop the steal,’” begin seizing voting data and order a new election.

“Clearly, an unlawful combination and conspiracy in multiple states (indeed, in every state) has acted to deprive the people of the fundamental right to vote for their representatives in a clear, fair election,” Mr. Rhodes wrote, adding, “You, and you alone, are fully authorized by the Insurrection Act to determine that such a situation exists and to use the U.S. military and militia to rectify that situation.”

In text messages and social media posts ahead of the Capitol riot, other Oath Keepers members also discussed the possibility of Mr. Trump invoking the Insurrection Act. Two of them, Jessica Watkins and Kelly Meggs, the head of the militia’s Florida chapter, have been charged in connection with the attack.

And Mr. Rhodes sent armed men to a hotel in Virginia on Jan. 6 to await Mr. Trump’s order, which the militia leader said would nullify Washington gun restrictions and allow the group to take up arms and fight for the president.

The House committee, which has interviewed more than 850 witnesses, is charged with writing an authoritative report about the events that led to the violence of Jan. 6 and coming up with legislative recommendations to try to protect American democracy from a repeat. Though their recommendations are likely to garner widespread attention, they are not guaranteed to become law.

One such recommendation is almost certainly to be an overhaul of the Electoral Count Act, which Mr. Trump and his allies tried to use to overturn the 2020 election. In recent weeks, the panel has begun discussing whether to call for revisions to the Insurrection Act, which empowers the president to deploy troops to suppress “any insurrection, domestic violence, unlawful combination or conspiracy.”

The changes under discussion could add a higher and more detailed threshold for a president to meet before he could deploy troops domestically, including requiring consultation with Congress.

“Essentially, the former president threatened by tweet to send in the armed services to take over civilian governments, because he saw things that he didn’t like on TV,” Ms. Lofgren said, referring to Mr. Trump’s threats to invoke the Insurrection Act in response to racial justice protests. “That’s not really the history of the use of the act, and maybe more definition of terms might be in order.”

The last time lawmakers turned their attention to a potential overhaul of the Insurrection Act was after Mr. Trump threatened in 2020 to invoke it to crush protests that spread across the country after a white police officer killed Mr. Floyd, an unarmed Black man, in Minnesota.

“If a city or state refuses to take the actions necessary to defend the life and property of their residents, then I will deploy the United States military and quickly solve the problem for them,” Mr. Trump said then. White House aides drafted a proclamation to invoke the Insurrection Act in case the president followed through with the threat.

Civil rights advocates responded with alarm, and Democrats in Congress rushed to try to curtail Mr. Trump’s power.

A group of Senate Democrats led by Senator Richard Blumenthal of Connecticut proposed legislation that would have required that the president consult with Congress before deploying troops and clarified that the Insurrection Act could not be invoked to curtail civil rights. The bill went nowhere in the Senate, which was then controlled by Republicans.

The Democratic-controlled House added similar limitations to the annual defense policy bill last year, but the limitations were stripped out of the legislation before it became law.

Republicans have insisted that Congress should not change the Insurrection Act, arguing that consulting with lawmakers would slow down a president when swift action could be needed.

“A president would not be able to act quickly and decisively in the event of riots that are not being controlled at the state or municipal level,” Representative Doug Lamborn, Republican of Colorado, said during a floor debate in 2020, adding, “This would hinder and delay needed action to preserve domestic peace.”

Mr. Esper, who opposed the deployment of troops on American streets and was fired as defense secretary by Mr. Trump, also told a congressional committee in 2020 that he did not support altering the law.

“My view is there’s nothing that’s happened that strikes me as compelling to change it at this point in time,” Mr. Esper said, adding that the law had “endured well” over time.

The law dates to the early 19th century, when President Thomas Jefferson signed it amid concerns that Aaron Burr, his former vice president, was plotting to raise an army.

President Andrew Jackson used the act in 1831 to crush Nat Turner’s rebellion of enslaved people. President Abraham Lincoln invoked it during the Civil War. President John F. Kennedy used the law to send troops to enforce the desegregation of Alabama public schools, and President Lyndon B. Johnson invoked it to protect civil rights marchers in Selma, Ala.

President George H.W. Bush was the last commander in chief to put it into effect, during the 1992 Los Angeles riots.

Alan Feuer contributed reporting.