“This is yet another cruel attack on children, who the Trump administration has targeted again and again with its anti-immigrant policies,” said Madhuri Grewal, the federal immigration policy counsel for the American Civil Liberties Union. “The government should not be jailing kids, and certainly shouldn’t be seeking to put more kids in jail for longer. Congress must not fund this.”

The administration first proposed the rule last fall, allowing the public to comment on the potential regulation. It is scheduled to be published Friday in the Federal Register and would take effect 60 days later, though administration officials concede that the expected court challenge will probably delay that happening.

Withdrawing from the consent decree has been a personal objective for Stephen Miller, the architect of Mr. Trump’s immigration policy. The New York Times reported in April that Mr. Miller berated the former acting director of Immigration and Customs Enforcement, Ronald D. Vitiello, for not finishing the rule more quickly. Mr. Vitiello later had his nomination withdrawn by Mr. Trump, who said he was not tough enough for the job.

[The Flores agreement protected migrant children for decades.]

If the new rule goes into effect, the administration would be free to send families who are caught crossing the border illegally to a family residential center to be held for as long as it takes for their immigration cases to be decided.

Mr. McAleenan said families would be detained until they were either released after being awarded asylum or deported to their home countries. Some families might be awarded parole to leave the facilities while the courts decide their fate, he said.

Almost 475,000 members of families have crossed the southwestern border in the past 10 months, Mr. McAleenan said, a number he said was three times the previous record for a full year. He said the number of apprehensions of families crossing illegally was up 469 percent from the previous year.