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Of the parents the government has identified so far, 46 remain in immigration detention centers.

But such exhaustive protections, including home visits and the fingerprinting of every member of a household where a child will be residing, are slowing down reunifications, said the lawyer, Lee Gelernt.

Immigrant children now housed in a tent encampment under the new "zero tolerance" policy by the Trump administration are shown walking in single file at the facility near the Mexican border in Tornillo, Texas, U.S. June 19, 2018.

Numerous numbers are still in flux.

(END OPTIONAL TRIM.) In his ruling on June 26, Sabraw said that children can be separated at the border only if the adults with them present an immediate danger to them.

But they also acknowledged that they do not know the whereabouts of the parents of roughly 20 percent of the toddlers still in custody, and likely won't meet the July 10 deadline. The odds are particularly steep in cases where those parents have already been deported, as the government argued Thursday.

The American Civil Liberties Union received the list of the names of the almost 100 children under the age of 5 who were separated from their parents at the border, according to a group spokesman.

According to an administration official, the DOJ now believes the government is on track to reunify nearly all of the those currently eligible by tomorrow, CBS News' Paula Reid reports.

In the court filing, the Justice Department sought clarification on whether they have to reunite migrant kids with parents who were already deported and appeared to argue that would be too hard and time consuming.

During the hearing the ACLU also accused the Trump administration of missing 10 children in its count of those in its custody aged newborn to five. He and his two older siblings are now in NY, according to court filings.

Susan Church, a Boston immigration lawyer, said the government could release migrants who are seeking asylum on bond so that they can find their children faster.

Once these families are reunified, it's not clear where ICE can legally - or feasibly - detain them. There are reports that some migrants agreed to be quickly deported, believing it would speed up the recovery of their children - only to board a plane and realize that their child would be left behind.

In his comments on Thursday, Azar said that "under 3,000" minors were separated from their parents.

Due to those missing records, the Health and Human Services department has been plunged into a messy, laborious process to determine which children were separated from their parents at the US-Mexico border, and which arrived in the country unaccompanied. In the case in D.C. court, parents have complained that federal officials have failed to provide adequate contact between the three parents and their kids.

The filing contained a description of steps undertaken by Health and Human Services to comply with the court order including deploying 115 additional personnel to the field, and contracting with 100 reunification managers who are deploying Friday and Saturday.