(CNN) Dozens, if not hundreds, of parents separated from their children at the border may have already been deported.

A federal judge said on Monday that, at least for now, more couldn't join them.

San Diego-based US District Judge Dana Sabraw ordered the US government to temporarily pause deportations of reunited families to allow attorneys time to debate whether he should more permanently extend that order.

Sabraw granted the request from the American Civil Liberties Union, which is representing immigrant parents who were split from their children in a federal lawsuit.

The judge has already ordered the government to reunify affected families, many of whom were affected by President Donald Trump's now-reversed "zero tolerance" border prosecution policy. Sabraw made the ruling at the top of a status hearing Monday to track the government's progress.

Sabraw ordered the pause to allow for a full written argument on the ACLU's request to pause deportations of parents for a week after reunification, which lawyers say would allow parents to fully consider a heart-wrenching choice: Be deported with their child, or have their child remain in the US to pursue a possible right to stay here permanently.

The ruling could impact a number of families. At the hearing the government confirmed for the first time how many parents and children in government custody have been matched up, at least preliminarily.

According to the numbers, 71 children separated at the border still have parents that are yet to be identified and located -- 20 days after Sabraw first ordered the government to put the families back together.

There were 2,551 total children aged between 5 and 17 separated from their parents at the border, according to the government. There are hundreds of children whose parents have yet to be accounted for, aside from the 71 whose parents have not yet been identified.

There are 1,609 parents of those children still in detention with Immigration and Customs Enforcement, Assistance Secretary for Preparedness and Response at HHS Commander Jonathan White testified.

That means that potentially hundreds of parents have either been deported or released already, or that they could be in federal or state criminal custody.

The government is expected to provide information about those categories of parents later this week.

Reunifications for children aged 5 and older has already begun, White confirmed.

Of the 1,609, HHS has already signed off on 1,317 that raise no red flags for safety or parental relationship. ICE also has to sign off: ICE has cleared 918 of those, and have found 51 are not cleared. Another 348 are pending clearance, White added.

Judge reminds attorneys of the stakes

The hearing represented the first time Sabraw, a George W. Bush appointee, showed frustration with the government on executing his order to reunify families.

At issue was the government's understanding that separating the families in the first place violated their rights as a family.

Sabraw reiterated his points from a memo over the weekend, in which he blasted the Health and Human Services Department for saying his order to streamline reunions would jeopardize children.

Sabraw called the declaration from HHS preparedness and response chief of staff Chris Meekins "deeply troubling in many respects ... completely unhelpful and doesn't get to the issues in this case."

In a lengthy monologue, Sabraw reiterated that what he called an "exasperating" filing was out of bounds, and he disputed Meekins' insistence that HHS was focused on the welfare of the child.

"By HHS being wed to a system that is not meant for this kind of case, this context, it is inviting a process of delay at the expense of children and parents which is not in the best interest of children. That's the plain reality," Sabraw said.

Sabraw did note that the Justice Department filing that followed up went a "long way" to address his concerns and called the later filing over the weekend a "good plan." He also praised White after the official answered the attorney's questions at length.

The government attorney at the end of the hearing invited Sabraw to visit an HHS facility caring for children, if he would like to, for full transparency. The judge indicated he appreciated the offer, but said it was beside the point.

"No matter how nice the environment is, it's the act of separation from a parent, particularly with young children, that matters, and it's time that is the issue," Sabraw said.

Pausing deportations

The ACLU argued that the week would be necessary for parents to have time to fully consider the decision whether to have their children deported along with them.

The ACLU's filing was made earlier Monday morning, and Sabraw gave the Department of Justice a week to respond.

But in the meantime, he ordered a "stay" of deportations until that issue can be litigated.

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Lawyers for the ACLU said their motion was due to "the persistent and increasing rumors -- which Defendants have refused to deny -- that mass deportations may be carried out imminently and immediately upon reunification." They argue this issue is "directly related to effectuating the Court's ruling that parents make an informed, non-coerced decision if they are going to leave their children behind."

"A one-week stay is a reasonable and appropriate remedy to ensure that the unimaginable trauma these families have suffered does not turn even worse because parents made an uninformed decision about the fate of their child," the ACLU's lawyers added.

In court, the government raised the possibility that his earlier order to pause deportations of reunified families for at least a week to allow for further arguments could cause problems. DOJ attorney Sarah Fabian said she would have to confer with officials, but noted space to house the families cleared for deportation once they're reunified could be a problem.

Sabraw said that simply could not be the case.

"The reunifications should continue in accordance with Commander White's plan and the idea that it would slow down or stop for other logistical reason due to a stay of trying to deport families immediately upon reunification, that's not an option," Sabraw said. "That just shouldn't be happening. There's no reason that I can think of where that can result in unhinging the reunifications underway. ... If space is an issue, the government will have to make space."