PIEDRAS NEGRAS, Mexico -- Patience was wearing thin Thursday for some of the 1,600 Central American migrants spending their fourth day at an improvised shelter in the Mexican border town of Piedras Negras, across from Eagle Pass, Texas.

Facing a long wait and a somewhat harsh welcome in Piedras Negras, in the northern state of Coahuila, some migrants asked to return to their home countries; the largest single group of those returning were from Honduras.

A large police force stood guard outside the unused factory complex where the shelter is located, about 5 miles (8 kilometers) from the border. A chain-link fence rings the perimeter of the shelter.

Federal and state officials confirmed that migrants without Mexican humanitarian visas weren't being allowed to leave the shelter, and those allowed out temporarily were taken in vans under police escort in groups of about a dozen to a nearby store to buy supplies, or to the U.S. border to file asylum claims.

U.S. officials are "metering" asylum claims, accepting only about a dozen per day because they say the facilities at Eagle Pass are at capacity.

Some migrants, especially those from Nicaragua, were willing to wait, trusting their asylum claims would be approved.

A Nicaraguan computer engineer said he left because of repression by the government of President Daniel Ortega. He didn't want to give his name because he feared reprisals against his wife and children, who remain in Nicaragua.

"We don't have a problem crossing to the other side, Nicaraguans are very well received in the United States, a lot of people have gone over and have gotten asylum," said the engineer.

He said he also didn't mind being kept inside the shelter.

"We have to wait because we aren't familiar with this place," he said through the chain-link fence. "We know it's dangerous because of the gangs and the kidnappings. I feel okay here inside, because I don't know anybody on the outside, anyway."

Previous caravans had travelled to the border city of Tijuana, but tensions there apparently played a role in this group's decision to go to Eagle Pass.

The U.S. Department of Homeland Security vowed that the "lawless caravan" would not be allowed in and has beefed up security at the relatively small border crossing.