A female migrant seeking asylum in the United States died on Christmas Day in government custody when she crossed the Gateway Bridge in Texas with her family, before reportedly succumbing to acute kidney failure.

The 41-year-old Congolese woman arrived at an official port of entry in Laredo, Texas, early on Tuesday afternoon, according to US Customs and Border Protection.

She came with paperwork that documented a “previous medical condition”, CBP said. The agency's medical personnel cleared her to be detained overnight.

The agency's statement said the woman told CBP officers early on Wednesday that “she was suffering from abdominal pain and had vomited”. The agency said it contacted emergency personnel “immediately” and had her taken to a local hospital.

According to information CBP gave members of Congress, the woman was diagnosed at the hospital with acute kidney failure. A congressional aide who spoke on condition of anonymity provided details to the Associated Press. CBP did not identify her illness in its public statement.

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“The subject's health declined rapidly and she passed away at the hospital”, CBP's public statement said.

She was travelling with her husband and two children, who were subsequently released.

Agents at official crossings between the US and Mexico have stopped tens of thousands of asylum seekers from entering the country under policies enacted by Donald Trump's administration, limiting crossings at many ports to just a few people daily and forcing others to wait in Mexico.

CBP told Congress that its officers admitted the woman and her family as part of the daily number of people allowed to enter at the Gateway to the Americas bridge. The agency says the Webb County medical examiner “has determined that the death is not suspicious, as the individual had a pre-existing medical condition”.

At least 11 people have died this year after entering CBP's custody, according to statements posted on the agency's website.

They include a 16-year-old teenager from Guatemala who died of the flu inside a Border Patrol cell in Weslaco, Texas, in May. Surveillance video later showed Carlos Hernandez Vasquez had been lying unresponsive for several hours despite the agency's claims that it carried out regular checks on him.