"We have a vital and historic mission here to protect these children", he said.
Alex Azar, the U.S. health secretary, said yesterday that officials were using DNA taken from cheek swabs of some 3,000 migrant children separated from their families and now under the agency's custody.
The administration has matched 86 parents to 83 children and 16 are not yet matched, Fabian said.
Still, the more than 2,000 children who were separated already are proving to be hard for the administration to grapple with.
A USA judge on Friday refused to grant the Trump administration a blanket extension of the deadline to reunite children separated from their parents at the border, instead acknowledging that more time may be justified only in specific cases.
The Department of Health and Human Services, which is responsible for both children taken from their parents and those who came to the US with an adult, is now trying to match families.
Now, the Trump administration is petitioning the court to be allowed off the hook for blowing past the 30-day deadline for reunification "in cases where parentage cannot be confirmed quickly", claiming that "potential traffickers" could be making "false claims of parentage" but providing no documentation of this happening.
He stressed that the department is seeking to meet a court-imposed deadline of next Tuesday to reunite some 100 detained children aged under five.
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The Department of Justice informed a federal judge in San Diego that the administration is in compliance with the judge's order requiring the end of family separations at the US-Mexico border, except under prescribed conditions, such as the safety of the child, and ensuring communication with separated parents and children as of Friday.
It also sought relief from a paragraph in the original injunction that prohibits the government from detaining adult migrants without their children, arguing it could be read to require the release of such detainees if they had not been reunified within the time frame set by the court.
"We have been deluged by thousands of doctors, lawyers and people who want to help", Gelernt said after the hearing.
The case is Ms. L et al v. U.S. Immigration and Customs Enforcement et al, 18-cv-428, U.S District Court, Southern District of California (San Diego). "To our knowledge, this is a cheek swab and is being done to expedite parental verification and ensuring reunification with verified parents due to child welfare concerns", one official told CNN.
Jonathan White, a Health and Human Services official, filed a declaration with the court that gives perhaps the most detailed account yet of what the government is doing and the hurdles it faces.
The latest information we have was provided to CNN by a U.S. government source: a map showing that the 2,047 separated unaccompanied minors who were in custody of the HHS Office of Refugee Resettlement as of June 25 were scattered across 16 states.
Government officials feel aggrieved in general at the stress caused by their practice, now halted, of separating parents and children in enforcing misdemeanor border-crossing crimes. "It's not here", Azar said, adding that migrant children are being well cared for in HHS facilities.