He told reporters that 14 illegal immigrants could not be reunited with children because some had criminal histories, some were determined not to be the parents of the children and one had a communicable disease.
The number is far less than the 54 the administration had suggested just a day earlier, and it underscores the government's continued struggles to clean up after President Trump's zero tolerance policy collapsed amid legal and public relations problems.
Now, one day before a Tuesday deadline, the administration says authorities expect to return just over half of the kids - but that they will need more time to figure out the rest. The administration has been given until July 10 to reunite separated children under 5 years old with their parents.
Abril Valdez of the ACLU of MI said the government was "vague" on the time and place of the reunifications that could come on Tuesday (Wednesday NZT) for two Honduran men he represents.
One immigration advocate told Reuters she was still awaiting details on when two under-five children would be back with their parents.
"Each step of our process is necessary to protect children", HHS official Chris Meekins, chief of staff in the Office of the Assistant Secretary for Preparedness and Response, told reporters on a press call.
Government officials touted the screening process for parents, including background checks and DNA tests.
In a court filing released on Tuesday, U.S. officials admit they may have taken a child away from a U.S. citizen at the southern border.
The ACLU's Gelernt said during a court hearing on Friday that it was "startling" that the government can not find some parents.
The government said 24 children are now not eligible to be reunited with parents "due to circumstances of the adults in question", 11 of whom are in criminal custody with either the U.S. Marshals Service or state jails.
A federal consent decree requires the government to release children from family detention facilities within 20 days.
In New York, attorney Michael Avenatti- the lawyer best known for representing the porn actress Stormy Daniels- said it took two tries plus a series of tweets Wednesday before he was allowed to see two Honduran girls, ages 9 and 5, who were separated from their family at the border in June, and sent to New York.
"Our message has been clear all along: Do not risk your own life or the life of your child by attempting to enter the United States illegally", the statement said.
In March, the American Civil Liberties Union filed a federal lawsuit challenging the Trump administration's separation of an asylum-seeking mother and her 7-year-old daughter.
Among the other remaining question marks is whether authorities can streamline their vetting process for the migrant parents - which ACLU attorneys have described as needlessly cumbersome - and whether the government can pass along the locations migrant families will be released from custody, so that charity groups can more quickly offer them support.
The distance between many children and their parent or parents have been coupled with logistical challenges and resulted in a major bureaucratic snag.
The government last week asked for more time to complete the reunification because it claimed it needed more time to ensure the children's safety and to confirm their parental relationships.
The administration faces a second, bigger deadline - July 26 - to reunite more than 2,000 older children with their families.
Orihuela said that the government knows where both J.S.R. and V.F.B. are and knows where their parents are being held.