The migrant caravan arrived Monday at Piedras Negras. It became the first caravan in months that headed towards Mexico instead of California.
The migrants said Wednesday that they are considering moving to another part of the border, where they may have a better chance of lodging a speedy asylum claim.
Mulling their next move from the dusty Mexican town of Piedras Negras, just south of the Eagle Pass crossing on the U.S. side, the latest group of migrants want to avoid a potentially months-long wait for a chance to plead their case for asylum.
Many say they are also waiting for a humanitarian visa from the Mexican government that could lead to local job opportunities, but are afraid of the area's hyper-violent Zetas drug cartel that has targeted migrants in the past.
"We can't stop here," said Oscar Lopez, a 33-year-old Honduran traveling with his wife and two daughters.
He said that his family fled death threats from gangs back home. "If we don't (cross) here, we'll go to another part of the border," he said.
The U.S. President Donald Trump said Tuesday that 3,750 additional military troops would be sent to the U.S.-Mexico border to support border agents and thwart what he described as "the tremendous onslaught" of U.S.-bound migrants.
Some 250 military personnel are being re-deployed from positions in Arizona to Eagle Pass "in response to migrant caravan activity currently approaching the Texas border," the U.S. Department of Defense announced Wednesday.
Thousands of mostly Central American migrants have been making the dangerous trek through Mexico to the U.S. border since October.
"These migrants face many risks," including organized crime, corrupt local police, and hostility from local residents, said Alberto Xicotencatl, who runs a shelter in the Coahuila state capital of Saltillo, about 250 miles (400 km) south of Piedras Negras.
Earlier this week, Coahuila Governor Miguel Angel Riquelme said he would not permit the caravan migrants to cross his state, but he did not detail any specific measures.
Hundreds of migrants from the first caravan remain stuck in the Mexican border city of Tijuana, many waiting their turn to legally enter and formally request asylum in the United States.
Local media reported that a group of migrants tried to climb a fence Monday to escape the factory building they are being held in but were forced to return.
The migrants will have to wait for months as immigration officials at Eagle Pass process only 12 to 15 requests per day.