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.