The tragedy unfolded when a Ford Expedition carrying 25 people smashed into a gravel truck near El Centro, California.
Officials say that the Ford SUV and a Chevrolet Suburban, which was carrying 19 people, were earlier caught on video entering the US as part of a migrant smuggling operation.
The Suburban immediately caught fire after entering the US, but all the occupants managed to escape and were taken into custody by Border Patrol officers.
The Ford Expedition continued, and was not being chased by agents when it crashed into the truck on Tuesday morning, Gregory Bovino, the Border Patrol’s El Centro sector chief told the Associated Press.
Ten of the 13 people who died in the accident have now been identified as Mexican nationals.
Authorities say that the two SUVs entered the US through a hole in the fence, built before Donald Trump’s wall, 30 miles east of the accident site.
Border Patrol officers say that a panel of eight steel poles were removed to allow the SUVs into California.
“Human smugglers have proven time and again they have little regard for human life,” said Mr Bovino.
“Those who may be contemplating crossing the border illegally should pause to think of the dangers that all too often end in tragedy, tragedies our Border Patrol Agents and first responders are unfortunately very familiar with.”
California Highway Patrol said that the Ford Expedition was designed to hold seven to eight passengers safely.
But in this case all of the seats had been removed apart form the driver and front passenger seats in order to pack people in.
Passengers in the SUV, both men and women, ranged in age from 15 to 53, and the driver was from Mexicali, Mexico.
The 68-year-old truck driver is from El Centro, California, and was hospitalised with moderate injuries.
Surviving passengers suffered minor to sever injuries, that included fractures and head trauma.
The Associated Press contributed to this report.
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