Mexico won't accept the "safe third country" status for migrants seeking refugee status in the United States, Foreign Affairs Minister Marcelo Ebrard said on Monday.

"Mexico has not under any circumstances accepted ... safe third country status for people who enter our territory seeking to enter the United States," Ebrard said at a press conference.

Such an agreement "would mean that all migrants, all, from anywhere in the world, who transit through Mexico to apply for asylum (in the U.S.) would be returned to our country with the only alternative of applying for refuge in Mexico; that is why we will not accept a treaty of this nature," he added.

The statement comes after Washington informed Mexico on Dec. 20 that all undocumented foreign migrants who cross the Mexico-U.S. border to seek asylum would be deported back to Mexico while their case was being reviewed.

However, Mexico's government will prioritize human rights in immigration matters, Ebrard added.

"Today, for migrants who transit the country, the experience is described as horrific. The orders we have from the president (Andres Manuel Lopez Obrador) is that the human aspect regulate all Mexican immigration policy," he said.