A seven-year-old Guatemalan girl died in American custody after being detained by US border police in New Mexico, The Washington Post reported on Thursday.

The girl who illegally crossed the border from Mexico along with her father and dozens of others died last week of "dehydration and shock," the newspaper reported, citing US Customs and Border Protection.

She had "reportedly had not eaten or consumed water for several days," the CBP told the Post, who said she began having seizures more than eight hours after being detained.

Emergency responders had measured her body temperature at 41 centigrade, the Post said. She died after being flown to hospital.

The name of the girl and her father have not been released.

The father is in El Paso, Texas awaiting a meeting with Guatemalan consular officials, the Post said, quoting CBP, which said it is investigating the incident.

President Donald Trump has made hard-line immigration policies a central plank of his presidency, drawing fire from critics who accuse him of demonizing migrants for political gain.

Much attention has been focused on caravans of thousands of Central Americans who have made their way to Tijuana, Mexico, just south from San Diego, California in a challenge to Trump, who criticised them as posing an "invasion".

But migrants fleeing poverty and gang violence also continue to cross over in New Mexico, Texas and Arizona after enduring dangerous treks through Mexico.

The CBP expressed its condolences for the death of the Guatemalan girl, the Post said.

"Border Patrol agents took every possible step to save the child's life under the most trying of circumstances," CBP spokesman Andrew Meehan said in a statement to the Post.

"As fathers and mothers, brothers and sisters, we empathise with the loss of any child."

Trump has vowed to build a wall on the border with Mexico, deployed thousands of US troops there and separated more than 2,000 migrant children from their parents as part of a "zero tolerance" policy on illegal immigration.