Mr. McAleenan said Monday that 538 children in Border Protection’s custody who were separated since May have been reunited with their parents. Those children were never sent to facilities run by the Health and Human Services Department.

At a shelter in downtown El Paso, Digna Emerita Pérez, a factory worker from El Salvador who spent a month in jail after her arrest for crossing the border without documentation, broke into tears when she found out that her son, 9, and daughter, 6, were in the same city.

But Nelvin Hernández, 48, a farm laborer from Honduras, who was released Saturday after a month in jail, was told his 17-year-old son, Noé, had been taken to Chicago. “My objective now is to find my son, regardless of what it takes,” he said Monday. “I’m nothing without my boy.”

But even before Monday’s announcement by Mr. McAleenan, the reality on the ground appeared far less simple than Mr. Trump or Mr. Sessions envisioned.

Administration officials said the zero-tolerance policy has been enforced in drastically different ways, depending on whether border communities have the resources to detain and prosecute new waves of immigrants.

A shelter in Tucson, Casa Alitas, takes in migrant families once American officials have released them into the country as their cases proceed. On Monday, Teresa Cavendish, who runs the shelter, said that government officials appear to be releasing many families into the United States together as a unit, rather than keeping them in detention — even when the families cross at unauthorized border points.

“These current families are very, very lucky,” she said.

At the towering federal courthouse in Tucson, the cases of dozens of recent border crossers were underway on Monday just as the Trump administration announced that it would halt the prosecution of people who enter with children.