Photos from the Rio Grande Valley reveal rooms packed with people sprawled on the floor, some penned in behind metal fences, others forced to stand.
In one photo, a man holds a cardboard sign with the word “help” to a cell window.
The situation was described as “a ticking time bomb” by a manager at one of the Texas centres.
The report by the Department of Homeland Security’s Office of Inspector General demands urgent action “to alleviate dangerous overcrowding and prolonged detention of children and adults”.
In one case, 71 men were packed into a a cell intended for 41 women.
The deaths of a father and his young daughter, pictured drowned on the banks of the Rio Grande river, have brought home the reality of the risks taken by the migrants.
US President Donald Trump insists the solution is to plough on with his plan to build a wall on the border with Mexico.
El Salvador’s leader has told Sky News a wall is not the answer, but said the deaths were “our fault” because his country is in such a perilous state.
At a detention centre in McAllen, Texas, the watchdog said there were more than 50 unaccompanied children younger than seven, “and some of them had been in custody over two weeks”.
Children at three centres had no access to showers, while some adults had not showered at all – despite being held for as long as a month – and were instead given wet wipes.
Detainees banged on windows and held up notes to show their time in custody as the inspectors looked around.
The US says nearly a quarter of a million people have been apprehended on the border from October 2018 to May 2019 – a 134% increase on a year before.
The watchdog visited five facilities and saw “serious overcrowding and prolonged detention of unaccompanied alien children, families, and single adults that requite immediate attention”.
It said thousands of people, including more than 800 children, were being held much longer than the 72 hours permitted.
Some adults at one centre were also being held in “standing room only conditions for a week”.
Border Patrol officials said people had deliberately blocked toilets with blankets and socks so that they could be released from the cells.
The Department of Homeland Security described the situation on the southern border as “an acute and worsening crisis” which is “overwhelming the ability of the federal government to respond”.
It said an average of 4,600 people a day had crossed or arrived at the border without proper documents in May 2019.
In May 2017, it was fewer than 700 a day.
Two tents capable of holding 500 people each have been put up in the Rio Grande Valley since the inspections, with plans for another by the end of July.
The DHS also said the number of unaccompanied children being held had fallen from nearly 2,800 to under 1,000 by 25 June.