Rodulfo Figueroa, an official with Mexico’s National Migration Institute, said the man in the brown jacket, whose name was not revealed, would be the only migrant returned to Mexico on Tuesday under the new policy, but that more are expected soon.

“We’re just reacting to a unilateral decision,” said Mr. Figueroa, a top federal migration official in the Mexican state of Baja California.

Since the Trump administration’s announcement of the new asylum policy, Mexican officials have been negotiating with their counterparts in Washington to define the conditions under which they would accept the migrants.

On Monday night, Tonatiuh Guillén López, the commissioner of Mexico’s National Migration Institute, said Mexico would only accept migrants from El Salvador, Guatemala and Honduras between the ages of 18 and 60. He also said that Mexico would only receive returned asylum seekers through the border crossing that connects Tijuana with San Diego, California.

The returned asylum seekers will be granted special four-month, multiple-entry visas that would allow them to travel to the United States for their court dates and then once again return to Mexico, Mexican officials said. Some of the returnees will already have one-year humanitarian visas which allow them to work and travel freely in the country. Asylum cases in the United States can take years to resolve, yet it remained unclear whether and under what terms the Mexican visas would be extended.

The American policy change applies to some asylum seekers who try to enter the United States at official crossings on the country’s southern border, or are apprehended on American soil after trying to cross illegally. But it will not apply to Mexican asylum seekers who might risk harm if returned to Mexico, the very place where they are claiming fear of persecution as grounds for their asylum claim.