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(CNN) —  

The Trump administration said Thursday it had reunited the bulk of the youngest migrant children separated from their parents at the border, but dozens still remain ineligible for reunification.

It is now starting to turn attention to the thousands of children aged 5 to 17 that need to be reunified with their parents in another two weeks.

The reunions – ordered nationwide last month by a federal judge in San Diego – have come in piecemeal tranches this week, as the government has scrambled to pinpoint the children eligible for return to their parents.

Joint statements from the Department of Health and Human Services, Justice Department and Homeland Security said that they had “completed” the reunification of 57 children with their parents as of early Thursday morning, but 46 were ineligible under “court-approved criteria.”

That included 11 who had criminal records – either charges or convictions – seven who were not the parent but could have been a different relative, one who had a false birth certificate, another accused of child abuse, another who wanted to live in a home with an adult with a criminal history, 12 who were already deported, 11 who are currently in state or federal criminal custody, one who cannot be found and one with a contagious disease.

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US District Judge Dana Sabraw originally ordered all children under 5 reunited by July 10. The government initially identified 102 children who fell in that category, but the number has fluctuated in recent days, as Sabraw’s order has essentially functioned as a judicially mandated audit of the morass of systems used by different federal agencies. One more was added since Tuesday because the parent who had originally declined reunification “changed his mind,” Immigration and Customs Enforcement official Matthew Albence said on a call with reporters.

The Justice Department told Sabraw on Tuesday officials had found that some parents were unfit for reunification because they had criminal histories, some had already been deported and still others had not yet been located. The administration uncovered one case in which the “parent’s location has been unknown for more than a year,” according to a recent court filing. In addition to the parents previously deemed unsuitable, another six parents had issues come up as background checks and DNA tests were completed between Tuesday and Thursday.

Thursday’s statement from federal agencies said that 12 adults had been deported and “are being contacted.” They may be reunited with children once they are located and contacted.

Albence, though, maintained that all of those parents agreed to be deported without their child. He alleged that the parents only wanted all along for their kid to stay in the US, and that is why they agreed to leave without them.

“These individuals had the opportunity to take the child with them when they were removed in the first place,” Albence said. “The reason they don’t is the reason they brought the child in the first place was to get the child to the United States.”

He also said that the parents will be given the option to have their child sent to them but would not be brought back to see them. Advocates for parents have complained that several of them may not have fully understood the paperwork they were signing when they agreed to their solo deportation.

“We don’t have the legal authority to bring these individuals back into the country for reunification purposes,” he said. “They have no lawful right to be here.”

In a response to the government’s filing, the American Civil Liberties Union, which had filed the lawsuit against the administration over separated migrant families, maintained that it does not believe the government fulfilled its obligation in time. As of the end of the day on the Tuesday deadline, 38 children had been reunited.

“If in fact 57 children have been reunited because of the lawsuit, we could not be more happy for those families,” said ACLU attorney Lee Gelernt. “But make no mistake about it: the government missed the deadline even for these 57 children. Accordingly, by the end of the day we will decide what remedies to recommend to the court for the non-compliance.”

Gelernt also asked in court Tuesday for detailed information about all of the parents deemed ineligible, so they could verify those rejections were, in fact, warranted and valid.

The judge had acknowledged in court Tuesday that after further investigation some parents may not fall within the class of those eligible for reunification with children at this point, but he reiterated to the Justice Department that the timetables he had ordered for reunifying families were “firm deadlines, not aspirational goals.”

The next hurdle

The looming and perhaps more significant question is how the administration will handle the much larger group of children 5 and older who are required to be reunited by July 26.

On that front, the judge has noted “there is a lot of work to do” on the older group of children and has ordered the Justice Department to provide an update Thursday on how many need to be reunited with parents.

“We are already beginning a process for reunifying children aged 5 to 17,” said Chris Meekins, the chief of staff for HHS’ response and preparedness office, in the call with reporters.

He noted some were already reunified with their younger sibling, and they are working to make arrangements for the rest.

“Our work to reunite the second group of families … continues,” added Albence, saying the process will be completed “as safely and as efficiently as we did with the first group.”

Meekins declined to provide a number of how many are left, but said that per the court proceedings, the government will be providing a list of names to the ACLU and their clients Thursday afternoon, so they can review the list.