Some families are being released into the United States. Border agents have not been able to turn away migrant families in South Texas because of a change in Mexican law that bans the detention of small children.

Administration officials point to a flurry of actions underway aimed at fixing what they say is a broken immigration system: improving communications between the Border Patrol and the health department, including whether the children being transported to the long-term centers are boys or girls; streamlining background checks for shelter employees; and vaccinating border workers against the coronavirus.

They are also accelerating efforts to get new facilities to care for children during the weeks and months that it takes to find relatives or foster parents. They are considering unused school buildings, military bases and federal facilities that could be rapidly converted into places acceptable for children.

And they are restarting a program in Central America that will allow children to apply for asylum without making the dangerous trek to the border. Mr. Trump ended the program, which Biden administration officials said would eventually reduce the flow of migrant children to the United States.

But all of that will take time. Meanwhile, officials say, they recognize that the pressure on Mr. Biden will only increase.

“At every step of the way we’re looking at where are the bottlenecks and then trying to eliminate those bottlenecks and yes it won’t be solved by tomorrow,” said Esther Olavarria, the deputy director for immigration at the White House’s Domestic Policy Council. “But if you don’t start to do each of these things, you are never going to solve the problem.”

Annie Karni and Maggie Haberman contributed reporting.

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