At least 39 people have died and dozens left injured after a fire broke out at a migration center on the US - Mexico border.

The blaze broke out at the National Institute of Migration (INM) in Ciudad Juarez late Monday night. 

Hours after the fire broke out late Monday, rows of bodies were laid out under shimmery silver sheets outside the facility in Ciudad Juarez, which is across from El Paso, Texas, and a major crossing point for migrants. 

Ambulances, firefighters and vans from the morgue swarmed the scene. Thirty-nine people died and 29 were injured and are in "delicate-serious" condition, according to the National Immigration Institute.

There were 68 men from Central and South America held in the facility at the time of the fire, the agency said.

Local media, citing unnamed sources, reported that there were dozens dead and around 40 victims hospitalized, some in serious condition.

The INM facility is located near the Stanton International Bridge, which links Juarez to El Paso, Texas. The Mexican city has seen the arrival of thousands of migrants, mainly from Venezuela, in recent months.

The fire broke out shortly before midnight, prompting the mobilization of firefighters and dozens of ambulances.