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(CNN) —  

A federal judge called the Trump administration’s slowness to track down migrant parents it had separated from their children and then deported “unacceptable,” saying the responsibility is “100%” on the government.

The stern admonishment from District Judge Dana Sabraw came a day after the administration argued that immigrant advocacy groups – not the government – should be responsible for tracking down the more than 500 parents it had separated from their children at the border and deported without them.

Sabraw said during a Friday phone hearing that if the government doesn’t track down the parents, it will have “permanently orphaned” their children.

“The reality is there are still close to 500 parents that have not been located, many of these parents were removed from the country without their child, all of this is the result of the government’s separation and then inability and failure to track and reunite,” Sabraw said.

“And the reality is that for every parent who is not located, there will be a permanent orphaned child, and that is 100% the responsibility of the administration,” he added.

Sabraw instructed the administration to name one or two officials to be a single point of command in the reunification effort, and to submit a detailed plan for how they will reunify children with parents either deported or, in a smaller number of cases, released into the US.

“In reviewing the status report it appears that only 12 or 13 of close to 500 parents have been located, which is just unacceptable at this point,” Sabraw said.

Justice Department said others should find the parents

In a court document Thursday, the Justice Department had suggested the American Civil Liberties Union should use its “network of law firms, NGOs, volunteers and others” to find the parents, using information the administration will provide.

“Plaintiffs’ counsel should ascertain whether each possible class member wishes to be reunified with his or her child, or whether he or she wishes to waive reunification,” the filing continued, adding that the ACLU would be “responsible for ensuring” the parents have the opportunity to get legal advice and consult with their children, with the government helping to “facilitate” those family communications.

The ACLU “would then be responsible for providing Defendants with a final, unequivocal, written confirmation of whether each possible class member wants to be reunified with his or her child,” the filing said.

The filing said the State Department has been enlisted to communicate with other countries’ officials on how to facilitate the reunification process.

As roughly two-thirds of the families separated by the administration have been reunited, the focus in an ongoing court case that ordered reunifications has turned to the more difficult cases – especially the hundreds of parents who were deported to their home countries alone.

The ACLU argued that shifting the responsibility from the government is unacceptable.

Sabraw did ask the ACLU to similarly establish a steering committee to oversee the effort that could work with the government, and to submit its own plan for reunifications by next week. ACLU attorney Lee Gelernt told the judge the organization had already put together a task force of global law firms and national and Central American nongovernmental organizations and could bring them into the court case.

To date, the ACLU says it is aware of 12 of the more than 500 parents who are in touch with attorneys and are trying to get their children back from the government. It questioned why the government has not made that clear to date and hasn’t made more progress on that front. The government said it received 13 names. The discrepancy was not clearly explained. In court Friday, Justice Department attorney Scott Stewart said he believed more had been located but could not give numbers.

The ACLU said it believes the government has had phone numbers for many of the deported parents for a significant amount of time, asking why those numbers weren’t either shared with it or used to contact the parents.

Sabraw ordered the administration to provide information to the ACLU on a “rolling basis” as quickly as possible, with information on all the parents due by August 10.

The administration has maintained that any parents deported without their children willingly left without them. Attorneys and immigrant advocates, however, have questioned whether the parents fully understood what they were agreeing to. The ACLU filed a lengthy collection of sworn statements from attorneys who say some parents were asked to sign documents they didn’t understand, felt coerced to sign or believed they were agreeing to something to get their children back.

The administration said Thursday that 410 children who remain in custody have parents who are no longer in the United States, but that is roughly 100 fewer than the overall total of deported parents.

At a Tuesday hearing, Commander Jonathan White of the US Public Health Service Commissioned Corps, who’s been heading up family reunification efforts, had said the parents of more than 500 kids from separated families are no longer in the US and may have been deported. White said at the time that 429 of those kids were in custody and 81 had been released to other sponsors.

CNN’s Nicole Chavez contributed to this report.