It is still unclear whether the government will seek to keep some of the families in detention long-term, or release them into the country using ankle monitors to track the parents. At least some have already been moved into family detention centers, where the government can legally hold them for up to 20 days, according to Bridget Cambria, a lawyer representing a Brazilian father and son who were reunited on Friday at one such facility, the Berks Detention Center in Pennsylvania.

Ms. Cambria said that Immigration and Customs Enforcement had flown the father from El Paso to Chicago, first to meet his son, and then flew them together to the detention center, which is near Reading, Pa. While the young boy seemed happy on Friday, an unknown future awaited the family, she said.

“Sitting with him today, he looked 1,000 times better than he did before,” Ms. Cambria said. “He wouldn’t let go of his dad, but he should be able to be in a community-based environment to deal with the trauma he has gone through and not be sitting in detention.”

She said she represented another Brazilian father and his son, 16, who was in Chicago; they, however, had a different outcome. They both were released to a sponsor in New England and prepared to apply for asylum.

The government’s plan was filed after a hearing in a lawsuit against the government over its family separation practice, and a chaotic week of down-to-the-wire reunions of a small subset of the separated children — those under 5 years old — with some false starts and delays.

The administration faces a much more daunting task ahead. Only 57 children under the age of 5 were reunited in the first phase, while 2,551 other children remain in custody, according to the latest government estimates.

Judge Sabraw on Friday laid out a set of intermediary deadlines, intended to prevent the last-minute execution of the first phase. He said that the government must confirm all parent-child relationships by July 19, a week before the final reunification deadline, and give at least 12 hours’ notice before a reunification of the location and identities of the parent and child.