In addition, some migrants, facing long waits in Mexico as their immigration cases unfold in the United States, are giving up and going home. The International Organization for Migration chartered several buses over the past two weeks to transport about 140 migrants back to Guatemala and Honduras. None of them had planned to seek asylum in the United States, I.O.M. officials said.

The first people returned to Nuevo Laredo under the Remain in Mexico program were sent across the border from the neighboring city of Laredo, Tex., on Tuesday: 10 Cubans and Venezuelans.

Reinier, 38, another Cuban asylum seeker, was among them. Though he had been forewarned of the policy, returning to Nuevo Laredo was “a blow,” he said, adding that he would have preferred to remain in American detention because it was safer.

During the six weeks he had waited in Nuevo Laredo for his appointment, he rarely left the shelter because of the danger on the streets. Now he said he had to endure two more months in Nuevo Laredo before his first court date.

The return of the migrants here this week has followed a pattern: They are escorted halfway across the border bridge by American border officials, who hand them off to Mexican border officials. After the migrants are processed, they are released without any guidance or further assistance from the government.

“I felt abandoned, unprotected,” Reinier said in an interview at the Nazareth shelter, also withholding his last name to protect his family back in Cuba.