A few days after the election, William Teer, who runs the Texas Three Percenters, a local far-right militia group, wrote to President-elect Donald J. Trump with an offer: His organization could help Mr. Trump carry out his plan to deport millions of people who are in the United States illegally.

“In support of our nation’s commitments to lawful immigration practices, I wanted to extend my willingness to assist, in cooperation with local law enforcement and community programs, to promote the safety and security of our state,” Mr. Teer wrote. “I am available for further discussion.”

He said Mr. Trump had yet to responded. A spokesperson for Mr. Trump’s transition team said the mass deportation plan would use state and federal resources, not private ones. But Mr. Teer’s offer was one of several recent efforts by far-right organizations, including some that have a history of taking it on themselves to patrol the border with Mexico, to insert themselves into the deportation plan.

Richard Mack, the founder of a group of hard-right sheriffs, said on television last week that if members of his organization assisted with the initiative, it would make it “a lot easier and a lot cheaper and a lot more effective.” And last month, members of other militia-style groups also volunteered their services, with some discussing in private group chats their desire to get involved.

The push by some militia groups to help Mr. Trump reflects how one of his signature policy proposals mirrors ideas that once existed solely on the fringes of American politics. Militia groups, especially in border states, have a long history of supporting enforcement efforts, sometimes taking migrants into custody on their own and turning them over to lawful authorities in agencies like the U.S. Border Patrol.