Once the president makes a proclamation identifying who is barred by the new regulations, an official said, those people could apply for two other, smaller programs that are much less likely to result in them being allowed to stay in the United States.

An administration official who briefed reporters said the two programs would satisfy the United States’ treaty obligations — a claim critics say is not true. The official, who spoke on the condition of anonymity to provide details of the rules before they are published, said the new regulations were supported by laws that gave the president broad authority to control who entered the United States.

The Immigration and Nationality Act says the president “may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate.”

In writing the Supreme Court’s decision upholding the president’s travel ban this summer, Chief Justice John G. Roberts Jr. said the immigration act “exudes deference to the president in every clause.”

Mr. Trump has fumed at his advisers for months about the surge of immigrants crossing into the United States from Mexico. Enraged by the caravan of several thousand migrants that began forming in Honduras and has been slowly making its way to the United States-Mexico border, he ordered more than 5,000 active-duty troops to the border to prevent the migrants from crossing.

By early this week, that caravan still had about 4,000 or 5,000 people and had made it to Mexico City. Smaller caravans of several hundred people each are reportedly also headed toward the United States.

Since taking office nearly two years ago, Mr. Trump has railed against what he calls weak laws that allow migrants who are caught crossing illegally to claim asylum under false pretenses and then be released into the United States, sometimes for years, as they wait for the courts to determine the validity of their asylum claim.