(CNN) — The Trump administration says immigrant advocacy groups should be responsible for tracking down the more than 500 parents it separated from their children at the border and deported without them.

In a court document filed Thursday as part of the ongoing lawsuit over separated families, the Justice Department 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 (the ACLU) should use their considerable resources and their network of law firms, NGOs, volunteers, and others, together with the information that Defendants have provided (or will soon provide), to establish contact with possible class members in foreign countries,” wrote lawyers for the administration, which is the defendant in the case.

“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 ACLU would be “responsible for ensuring” the parents have the opportunity to get legal advice and consult with their child, with the government helping to “facilitate” those family communications. 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 did note 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 that were deported to their home countries alone.

San Diego-based District Judge Dana Sabraw has made clear that he wants to focus on those parents next, and agrees with the ACLU that they should be contacted to see if they want their children returned to them.

A Friday afternoon hearing is expected to focus on the issue, including how the process should proceed.

The administration is proposing that every Monday, the ACLU would share any new information about the parents it locates, including whether they wish to be reunited with their children.

But the ACLU says while they are eager and ready to help, shifting the responsibility off the government is unacceptable.

The ACLU argued that the government “must bear the ultimate burden of finding the parents.”

“Not only was it the government’s unconstitutional separation practice that led to this crisis, but the United States Government has far more resources than any group of NGOs,” ACLU attorneys wrote.

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 kids back from the government. They 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 is not clearly explained.

In fact, 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 them or used to contact the parents.

“Assuming the Government has had phone numbers all this time for some or many deported parents, those phone numbers should have been provided to Plaintiffs and the Government itself should have been reaching out to those parents for purposes of reunification,” the ACLU’s lawyers wrote. “In short, Plaintiffs understood the Court to allow the Government to miss the deadline for deported parents on the assumption that the Government could not possibly locate these parents before the deadline. As the Court is aware, the children with deported parents are suffering as much, if not more, than the children whose parents remained in the United States.”

The administration has maintained that any parent deported without their child had the opportunity to bring their kid with them but 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 or believed they were agreeing to something to get their child back.

Also central to the dispute over the process for finding the parents is the sharing of information, something the attorneys have sparred over for weeks.

The government continues to resist giving the ACLU the entire case files of separated parents for the groups to use to track down parents. Instead, they propose delivering a list of information that the ACLU has said was a non-exhaustive list.

The administration “should be taking the initiative to continually provide Plaintiffs with whatever useful information they possess,” attorneys wrote, rather than waiting to be asked for specifics.

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 less 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, 429 of those kids were in custody and 81 kids have been released to other sponsors.

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