(CNN) There are more than 2,500 children who could need to be reunited with their parents in the next two weeks after officials separated them at the border, according to the latest government estimate.

That number was revealed for the first time Friday as the government gave its first indications of how reunions of those thousands of parents and children could go.

There are about 2,551 kids age 5 and over in government custody who could be eligible for those reunions, officials wrote in a court filing Friday. The reunions of those children with their parents will occur in six to eight designated Immigration and Customs Enforcement facilities, according to the filing. And officials will use a new, streamlined vetting process to facilitate reunions by the court-ordered deadline of July 26, the filing says.

In a statement following the filing, the Health and Human Services Department noted that number could fluctuate as more is learned about the parents of those children and whether they are eligible to be reunited.

"This number represents the total possible cohort of minors who could potentially be subject to the court order, and, based on past experience, includes a significant number of minors who cannot or should not be reunified with the adults in question," said HHS spokeswoman Evelyn Stauffer.

The government noted that things will proceed differently for these reunions from the ones for the children under age 5, because of previous rulings in the ongoing lawsuit over family separations at the border and lessons learned from the earlier reunions, which numbered fewer than 60.

The new steps include not DNA-testing most of the parents and not background-checking every adult who will be living in the home with the reunified family.

Official warns of increased risk of child abuse

Even as they vowed to comply, officials went to great lengths to once again register their dismay at court-ordered provisions for the reunions, which they warned could put children's safety at risk.

In Friday's court filing, officials argued that when preparing for reunifications for children under 5, their background checks raised some red flags, including adults who were found not to be parents and some criminal concerns, like an adult in a home who had been accused of sexually abusing a young girl. At least three of the adults who were not parents were blood relatives, however -- two grandmothers and an uncle.

"My opinion is that the court's necessary truncating of the vetting process for class membership -- including the suspension of critical information-gathering through mandatory completion of family reunification packets -- materially increases the risk that HHS will reunify a child with a parent who will abuse them," wrote Chris Meekins, the chief of staff at HHS' office of preparedness and response.

Meekins wrote that he's fully committed to complying with the court's order. But he stressed that he doesn't agree with it.

"I do not believe that the placing of children into such situations is consistent with the mission of HHS or my core values," he said.

But even though the government has made this argument in public and in court, the judge in the case has maintained that because the government was the one to separate these families, it has an "obligation" to reunite them swiftly.

US District Judge Dana Sabraw indicated in a court hearing Friday that parental verification should be "common sense," saying that in many cases it may be through documents, it may be a "little girl is clinging to her parents screaming, 'Mommy, mommy,' all the time," or it may require DNA testing if those options don't work."

The judge indicated that his touchstone is the types of decisions ICE has made in the field for a long time, a general "comfort level" with whether the individual appears to be a parent.

But he reiterated that the government should not hold itself to the level of scrutiny it undertakes when someone who did not arrive with the child at the border comes forward to take that child out of custody.

Earlier this week, Sabraw called HHS' full procedures "backwards" for this situation, and said that "the parent has a right to be reunified."

"The parents are not applying. They don't have to prove that they're going to be a good sponsor," Sabraw said. "What the government has to look to is whether the parent is unfit or a danger."

A 'very different' process

The government's latest court filing summarizes the reunion plan going forward as follows:

• ICE will use between six and eight locations for reunification

• HHS will use streamlined vetting, as described above

• ICE will move those who fall into the class to locations for reunification

• HHS teams will conduct further interviews there to complete the vetting process, which will take about 15 minutes and include seeking "verbal confirmation ... of parentage as well as the desire to reunify with the child."

• If the parent is confirmed as eligible, HHS will move the child to the same location as the parent within 24 to 48 hours

• The child will then be transferred to ICE custody, and ICE will reunite them with the parent.

The filing came shortly after the hearing Friday, where government attorneys, American Civil Liberties Union lawyers and a federal judge hashed out the next steps in the court-ordered reunion process. Sabraw ordered the government last month to stop most immigrant family separations at the border and reunite the families it had already split up.

"I think this process going forward will be very different," Justice Department attorney Sarah Fabian said during the hearing.

The ACLU's Lee Gelernt reiterated a request to have more notice from the government about reunions before they occur, to make sure resources are in place to help families.

"You promised to get us some of the time and locations of the reunions," Gelernt said, "and we got zero."

Sabraw said that going forward, the government should provide 12 hours' notice before a reunification.

A number of key but as yet unresolved issues also came up during the hearing, including how and when the government should use DNA testing to verify parentage, the time frame for reuniting children with deported parents and whether the government will cover all the costs of reuniting families.