But migrants’ advocates and human rights activists say the Mexican government would be ill prepared to handle the sudden and significant surge in asylum petitions that would result from a safe third country agreement.

Mexico’s asylum system is already overwhelmed by the growing numbers of immigrants that have sought sanctuary in recent years, the advocates contend. Moreover, they say, Mexico remains a very dangerous place, with weak law enforcement and judicial systems incapable of providing adequate protections for migrants who are in transit or are seeking to stay.

“The fact is that Mexico is not a safe option for many people, least of all migrants and asylum-seeking families,” said Michelle Brané, director of the migrant rights and justice program at the Women’s Refugee Commission, an advocacy group. Such a deal, she said, would be “nothing more than another attack by the Trump administration on women, children and families seeking safety at our border.”

In recent years, violence in Central America has driven tens of thousands of people to migrate to the United States to seek protection.

A far smaller but increasing number of Central Americans and migrants from other countries have sought sanctuary in Mexico. In 2016, the last full year for which statistics are available, nearly 8,800 people applied for asylum in Mexico, almost seven times as many as in 2013, according to Mexico’s government. About the same number applied during the first eight months of 2017.

The idea of a safe third country agreement with Mexico has not been the exclusive domain of Republicans. According to Mexican officials, Obama administration officials brought up the idea informally in negotiations with their Mexican counterparts, but the initiative went nowhere.

The Trump administration has championed the notion more forcefully, Mexican officials say. Some Republican legislators in Washington have even pushed a bill that would allow the United States to return Central American asylum seekers unilaterally to Mexico — without the need for a bilateral agreement, according to a summary of the bill from the House Judiciary Committee.