Mexican officials stepped up efforts on Tuesday to register a dwindling group of hundreds of largely Central American migrants who are moving through Mexico toward the United States, seeking to disperse the "caravan" that has drawn the ire of U.S. President Donald Trump.

Trump, who has long sought to take a tough stance against illegal immigration, has railed against the caravan that has worked its way from the Guatemala-Mexico border in the past 10 days. Over the weekend, and again on Tuesday, he reiterated threats to torpedo the North American Free Trade Agreement (NAFTA) if the migrants are not stopped.

In response, the Mexican government said on Monday the migrants in the caravan are undergoing an "administrative procedure" — a process that officials said would determine whether they had the right to stay in Mexico or would be returned to their countries of origin.