Sarah Fabian, a Justice Department lawyer, said that as of this weekend, there were 102 children under five who were still in government custody and separated from their parents.
Administration for Children and Families at the US Department of Health and Human Services The family reunification process has so far been beset with complications.
Azar said the logjam was due to previous policies and court decisions that prevent migrant families from being held in detention for extended periods.
On Friday, the administration asked the judge for more time but Sabraw said he was sticking to the deadline unless there was a good case for certain exceptions.
However, she added, "There are some groups for which the reunification process is more hard". The government has until 26 July for older children.
Two such background checks have already found parents with charges of kidnapping/rape and child cruelty, according to the government.
Judge Sabraw also scheduled a status hearing on Monday morning, saying he hopes an agreement can be reached regarding whether Tuesday's deadline will need to be extended.
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Sabraw had mandated that the government reunite children younger than five with their parents on June 26. In a statement, an administration official said its priority was "to ensure the safety of the children in its custody".
This isn't a ideal equation; we don't know whether the children released from HHS custody were reunited with parents - only that they're no longer in one of the agency's shelters.
The American Civil Liberties Union received the list of the names of the almost 100 children under the age of 5 who were separated from their parents at the border, according to a group spokesman.
The motion also asks for clarification on the class of unauthorized immigrants that the order applies to, including whether it includes parents who have already been deported. The separations were in place from early May until Trump stopped the practice last month in the face of intense criticism.
Much of the problem reportedly stems from incomplete records on the immigrant families who were arrested at the border.
Health and Human Services Secretary Alex Azar said Thursday there were "under 3,000" children separated from their parents. HHS typically uses birth records to match children and their parents. According to HHS, it's because the number of immigrant children in the agency's care is always in flux - and because they are working with other agencies to cross-check the numbers they have.
The government's court documents describe an extensive and painstaking effort to collect information between the Departments of Homeland Security and Health and Human Services; verify the parentage; and assess the parents' "fitness" to receive their children. Apprehensions of illegal border crossers slumped in June, as they typically do in the hot summer months, though at more than 42,000, the monthly tally is almost double what it was in June 2017.