A seven-year-old Guatemalan girl died in US custody after being detained by US border police in the state of New Mexico, The Washington Post has reported.

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

The child, whom CBP said "reportedly had not eaten or consumed water for several days", began having seizures over eight hours after being detained, was flown to a hospital and died there, the Post said.

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

He 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.