The rule adds to a growing list of policies limiting who is eligible for an asylum program that has diminished under President Trump. The administration already tried unsuccessfully to bar any migrant who crossed the southern border between the ports of entry from obtaining asylum and directed agents at the border to limit the daily number of migrants who can be processed at those ports.

The administration also recently began deporting asylum seekers to Guatemala if they failed to apply for asylum there under a deal with that Central American country’s government. The United States is preparing to put a similar deal in place with Honduras to handle additional asylum seekers, who would be required to apply there.

The administration last month also proposed charging asylum seekers $50 for their applications, a move that would make the United States one of four countries to charge for asylum. More than 53,000 migrants have been returned to Mexico to wait while their asylum cases make their way through the immigration system.

The White House and the Department of Homeland Security have argued that few migrants are actually granted asylum, that those who are denied often stay in the United States illegally and that the country’s immigration system has been overwhelmed by a surge of asylum-seeking families in recent years.

The new rule would most likely limit the number of asylum seekers who have a chance to make their case in immigration court — a court system that this year topped more than one million cases. Arrests at the southern border have declined from more than 144,000 in May to more than 40,000 in November, but the administration has continued to find ways to limit migration.

“This administration simply wants to limit legal immigration, and they’ve been very creative in going up and down and finding all these small levers,” said Barbara Strack, a former chief of the refugee affairs division at United States Citizenship and Immigration Services under Presidents George W. Bush and Barack Obama.

Even migrants who have had prior convictions expunged or modified would be subject to the new rule. Such migrants would need to prove that their sentence was not changed in order to gain legal status in the United States. Under the rule, immigrants would still be able to prevent their deportation if they could prove that they had a fear of torture or persecution, a much higher bar to clear than the standard for asylum protections.