The number of border crossings appears to have slowed in recent weeks, possibly as a result of a crackdown by the Mexican government under pressure from President Trump, but the numbers remain high compared to recent years. The overcrowding crisis has been unfolding invisibly, with journalists and lawyers offered little access to fenced-off border facilities.

The reports of unsafe and unsanitary conditions at Clint and elsewhere came days after government lawyers in court argued that they should not have to provide soap or toothbrushes to children under the legal settlement that gave Ms. Mukherjee and her colleagues access to the facility in Clint. The result of a lawsuit that was first settled in 1997, the settlement set the standards for the detention, treatment and release of migrant minors taken into federal immigration custody.

Ms. Mukherjee is part of a team of lawyers who has for years under the settlement been allowed to inspect government facilities where migrant children are detained. She and her colleagues traveled to Clint this week after learning that border officials had begun detaining minors who had recently crossed the border there.

She said the conditions in Clint were the worst she had seen in any facility in her 12-year career. “So many children are sick, they have the flu, and they’re not being properly treated,” she said. The Associated Press, which first reported on conditions at the facility earlier this week, found that it was housing three infants, all with teen mothers, along with a 1-year-old, two 2-year-olds and a 3-year-old. It said there were dozens more children under the age of 12.

Ms. Mukherjee said children were being overseen by guards for Customs and Border Protection, which declined to comment for this story. She and her colleagues observed the guards wearing full uniforms — including weapons — as well as face masks to protect themselves from the unsanitary conditions.

Together, the group of six lawyers met with 60 children in Clint this week who ranged from 5 months to 17 years old. The infants were either children of minor parents, who were also detained, or had been separated from adult family members with whom they had crossed the border. The separated children were now alone, being cared for by other young detainees.

“The children are locked in their cells and cages nearly all day long,” Ms. Mukherjee said. “A few of the kids said they had some opportunities to go outside and play, but they said they can’t bring themselves to play because they are trying to stay alive in there.”