“While congress continues to do nothing,” he wrote on Twitter, “@realDonaldTrump’s administration uses every tool in the toolbox to try and solve the crisis at our southern border.”

In a Supreme Court brief in the case, the solicitor general, Noel J. Francisco, said the new policy was needed to address “an unprecedented surge in the number of aliens who enter the country unlawfully across the southern border and, if apprehended, claim asylum and remain in the country while their claims are adjudicated.”

Under the policy, which was announced July 15, only immigrants who have been denied asylum in another country or who have been victims of “severe” human trafficking are permitted to apply in the United States. “The rule thus screens out asylum seekers who declined to request protection at the first opportunity,” Mr. Francisco wrote.

Under the rules, Hondurans and Salvadorans must seek and be denied asylum in Guatemala or Mexico before they can apply in the United States. Guatemalans must seek and be denied asylum in Mexico.

Migrants from Honduras, El Salvador and Guatemala have made up the vast majority of asylum seekers who have tried to enter the United States in record numbers this year. The Border Patrol has arrested 419,831 migrant family members from those three countries at the southwestern border so far this fiscal year, compared with just 4,312 Mexican family members.

The administration made the unilateral move after months of pushing Guatemala and Mexico to commit to going along with the plan. Mr. Trump went as far as to threaten both countries with tariffs unless they did more to halt the migration.

The administration struck such a deal with Guatemala in July that would force the country to absorb Central American migrants. But Guatemala’s Constitutional Court has ruled that it needs further approval, and the countries are still working on a plan to carry it out the deal.