“To those of us whose job it is to promote the health and safety of children, this is a shocking directive,” said Amy Cohen, a psychiatrist who consults for the Flores team and regularly interviews children at shelters. “It violates every tenet of basic child welfare practice and will further harm the medical and psychological health of children fleeing extraordinarily dangerous circumstances in their home countries.”

After being intercepted by Border Patrol, migrant children are sent to government-licensed shelters across the country, where they remain until a sponsor — typically a relative already living in the United States — can prove that she or he is fit to care for the child. Nearly 41,000 migrant children have been taken into government custody this fiscal year that began Oct. 1, about 60 percent more than last year. Federal officials have predicted that a record number could arrive by year’s end.

Critics of the plan to reduce services said costs had been driven up because children were being held for protracted periods of time, instead of being released to family or friends. The current length of stay, ranging from about 50 to 75 days, is twice as long as it was during the Obama years, according to Dr. Cohen.

“I have interviewed children held for more than a year despite a fully competent and willing family sponsor,” Dr. Cohen said. “I interviewed an increasingly desperate child who’d been there for four months despite having a close, safe relative fully prepared to take her.”

This is often because of rigorous standards the government imposes before it releases children to a private sponsor. In some cases, sponsors’ homes are deemed by government-contracted social workers to be inadequate to receive a child, often because they are very modest. In other cases, potential sponsors, such as aunts and uncles, struggle to prove a pre-existing bond with a child for lack of such items as a photograph — even when both the child and family members back home confirm a connection.

In testimony before a House Appropriations subcommittee in April, Health and Human Services Secretary Alex Azar said that the system was running out of beds and cautioned that at the current pace of arrivals, available funding would not suffice. “We need help,” he said.

Educational and recreational activities ensure that children are engaged during much of the day, and help to avert behavioral problems, shelter operators say. At least one operator said he would resist canceling educational and recreational activities, which were important for the children’s well-being.

“We have not and we are not going to curtail recreation and education. We just can’t do that,” said Kevin Dinnin, president of BCFS, the second-largest shelter network, which houses about 1,000 children in facilities in Texas. “We will have to use reserve funds until the government figures out what they are going to do.”