More than 2000 children were separated from their parents by US immigration authorities at the border this spring before US President Donald Trump reversed course on June 20 amid an global outcry.
And activists, for their part, have described a "bureaucratic wall" that has prevented detained parents from finding and contacting their children.
Nine have parents who were removed already from the US.
This plan bypasses the lengthy "sponsor" process that is required to release an unaccompanied immigrant child from Health and Human Services custody.
American Civil Liberties Union attorney Lee Gelernt sought assurances from the government on Monday (Tuesday NZT) that advocates would be in position to guide parents when they are released in a foreign land. Fabian explained that of the 102 children under 5 who have been identified, only 54 of them-possibly 59-would be reunited with their families on time.
The ACLU sued in March on behalf of a Congolese woman who was separated from her daughter for five months after seeking asylum at a San Diego border crossing and a Brazilian asylum-seeker who was separated from her son after an arrest for illegal entry in August near the Texas-New Mexico border.
But Gelernt took issue with the administration's "continued insistence on using the longer reunification process" - procedures HHS uses for children who arrive to the USA alone.
Amid enormous backlash and worldwide outcry, Trump reversed course on 20 June and said families should remain together until the parents' immigration proceedings are complete, a process that can take months. "This is a cruel and harmful policy that was aggravated by the Administration's lack of basic humanity in thinking ahead of time about how it would bring these families back together". They also note that DNA swabs are being utilized in order to quickly place the minors.
In the meantime, many of these children have had to face their immigration proceedings without their parents in court.
"There's no question that the parties are meeting and conferring", she said.
So far, the government has reunited four of the children in its custody, and expects to reunite another 34 by Tuesday's deadline.
"Let me be clear, HHS could have transferred every child in HHS care to a parent if we did not take into account child safety", Meekins said.
"The objective of the [Trafficking Victims Protection Act ] is to promote the best interests of the child and to reunite families", the ACLU had argued.
Five have parents still in ICE custody who could be released soon, but require more follow-up after a background check.
Federal officials said they are reunifying as many children as they can and attributed delays to "legitimate logistical impediments" that make it "impossible or excusable" to meet the court's deadlines. The two sides are due in court Monday. Eight other parents had serious criminal histories and the government found evidence of child abuse by another, according to the filing. Some parents are not eligible, the government said, because they have criminal records, were deemed to be unfit or, in one case, have a communicable disease.
"Let me put it this way: I think the government in the last 48 hours ... has taken significant steps", Gelernt said.