Lawyers given access by a judge said the children were ‘severely neglected’, BBC News reported.
One of them told the BBC that children were "locked up in horrific cells where there's an open toilet in the middle of the room" where they ate and slept.
Many parents crossing the US border, most of them from Central America, were separated from their children in 2018.
Separately, border patrol in Texas reported the deaths of seven migrants this week who had apparently attempted to circumvent the immigration system — including two babies and a toddler.
What were conditions like?
"There was nobody taking care of these children... they were not being bathed on a regular basis," Prof Warren Binford of Williamette University in Oregon told the BBC after visiting the Clint facility in Texas.
"Several hundred of the children had been kept in a warehouse that was recently erected on the facility grounds."
"The cells are overcrowded... there's a lice infestation there, there is an influenza outbreak. Children are being locked up in isolation with no adult supervision, who are very, very ill and they're just lying on the ground on mats."
Elora Mukherjee, another lawyer who visited the facility, told CBS News, "They were wearing the same dirty clothing they crossed the border with."
"It is degrading and inhumane and shouldn't be happening in America."
In a statement, the border authority acknowledged that the Clint facility was not suited to the task.
"US Customs and Border Protection leverages our limited resources to provide the best care possible to those in our custody, especially children," it said.
"As our leadership have noted numerous times, our short-term holding facilities were not designed to hold vulnerable populations, and we urgently need additional humanitarian funding to manage this crisis."
The agency said it had moved children to more suitable facilities as soon as space was available.
On Monday, Democratic Representative Veronica Escobar, who had been deeply critical of the reported conditions, said she had been told that only 30 children remained in the Clint facility.
Where are parents?
The separation of migrant children from their parents began in 2018 under a new ‘zero tolerance’ policy from President Donald Trump's administration. It saw nearly 3,000 children separated before it was suspended.
Under the policy, announced in May 2018, those who cross the border illegally were to be prosecuted — which required their children to be taken into care.
Yet the US Government Accountability Office has reported that neither the Department of Homeland Security nor the Department of Health and Human Services were aware of the policy before it was publicly announced, and so were not prepared for the increase in children being kept imprisoned.
There are also limits set by the US authorities on how many people can claim asylum each day, resulting in a waiting period that can last months.
Some migrants and their families are instead attempting dangerous crossings far from the official ports of entry, or relying on people smugglers to make the journey.
The seven people found dead this week by US Border Patrol included a woman and her three children who were thought to have died from heat exposure and dehydration, Reuters reported.
Two more men and an unidentified body were found on June 19-20 in two separate locations.