At least 39 migrants died in a fire that broke out at an immigration detention center in a Mexican city on the US border, the Mexican government said Tuesday.

The fire broke out shortly before midnight at the National Migration Institute (INM) facility in Ciudad Juarez, prompting the mobilization of firefighters and dozens of ambulances.

An AFP journalist saw forensic personnel remove a dozen bodies from the INM's parking lot, where several other bodies were laid and covered with blankets.

"The National Migration Institute (INM) of the Interior Ministry regrets the deaths -- so far -- of 39 foreign migrants, caused by a fire," an INM statement said.

A rescuer, who asked not to be identified because he was not authorized to speak to the media, said there were about 70 migrants, mostly Venezuelans, at the center.

Numerous migrants have been detained in the center in recent days after local authorities rounded up street vendors, some of whom were foreigners, from the area.

A Venezuelan woman who gave her name as Vinagly stood outside the immigration center, desperate for information about her 27-year-old husband who had been detained there.

"He was taken away in an ambulance," she told AFP, adding that her husband had documents allowing him to remain in Mexico.

"They (immigration officials) don't tell you anything. A family member can die and they don't tell you he's dead," Vinagly said, her voice cracking.

A heavy military and national guard presence blanketed the site early on Tuesday.