Mr. Trump’s tweets on Sunday threw new legal questions into the puzzle. Laurence H. Tribe, a constitutional law professor at Harvard, said in an email that the Supreme Court has repeatedly held that “the due process requirements of the Fifth and 14th Amendments apply to all persons, including those in the U.S. unlawfully.”

“Trump is making the tyrannical claim that he has the right to serve as prosecutor, judge and jury with respect to all those who enter our country,” Mr. Tribe said. “That is a breathtaking assertion of unbounded power — power without any plausible limit.”

The Fifth Amendment mandates the due process of law, and the 14th Amendment, in part, expanded due process rights for immigrants, with case law asserting those rights dating back to 1886. But Justice Department lawyers under both Democratic and Republican administrations have argued that noncitizens apprehended at the border lack due process protections, said Adam Cox, a law professor at New York University, and the Supreme Court has never clearly resolved the dispute.

Since Mr. Trump was elected, his administration has been working to expand the terms of a 1996 statute that allows immigration officials to quickly deport undocumented immigrants as well as those whose papers are believed to be fraudulent. The Trump administration has the ability to expand the statute to encompass the entire country and apply it to any noncitizen who has not been in the country for more than two years, Mr. Cox said.

“One of the things that is being considered is an expanded expedited removal to the full statutory limit,” he said, adding that “it is already true that a lot of people show up at the border get removed with no access to immigration courts or the judicial process.”

Mr. Cox said the president could be reacting to seeing a high number of people held in detention centers claiming they face harm back home. The White House did not immediately respond to a request for comment on whether the president knew the legal ins and outs of his demand.

“Many members of the administration seem to think that the high rate necessarily means a lot of fraud,” Mr. Cox said of asylum claims, “so what they could like to do is remove that process.”