Sen. Dick Durbin, D-Ill., on Sunday compared the more than 2,300 migrant children separated from their parents after crossing illegally into the United States to the boys’ soccer team currently trapped in a cave in northern Thailand.

“Hearts and prayers are with those boys in Thailand trapped in the cave,” Durbin said on NBC’s “Meet The Press.” “I hope our hearts and prayers are also with thousands of children – toddlers and infants – removed from their parents by the Trump administration under zero-tolerance.”

Durbin added: “They’re trapped in a bureaucratic cave too. So let’s not forget them.”

It's still not clear how many children have been separated from families under the zero-tolerance policy, or how many remain separated. Trump administration officials have said 2,342 children were separated from 2,206 parents between May 5 and June 9. Trump's order stopped separations on June 20.

About 520 children were reunited with their families within days because the improper-entry prosecutions were finished before the minors were turned over to the custody of Health and Human Services, which is responsible for caring for unaccompanied children. HHS Secretary Alex Azar told a congressional committee last month there were 2,047 such children in his agency's care.

On Thursday, Azar said there are somewhere "under 3,000" children who were believed to have been separated, but that includes kids who may have lost parents along the journey, not just parents who were detained at the border. He said none had been transferred to Immigration and Customs Enforcement custody yet.

A federal judge in San Diego who had been hearing the case of a woman separated from her child ruled on June 26 that the families must be reunited within 30 days of his order, and by July 10 if the children are younger than five.

But it's still not clear yet how that will work. Homeland Security has set up a staging area at the Port Isabel detention center in Texas where the parents can be detained until their children arrive. But it's not clear where they will go afterward — the three operational family detention centers are near capacity.

It's also possible not all parents will be reunited with their children; HHS has a strict set of guidelines the agency must follow to determine a suitable sponsor, including a home visit and a criminal background check.

Health and Human Services deployed more than 200 workers to review the cases of separated children. Azar said parents and children are being swabbed for DNA to match paternity and checks are being done as rapidly as possible to make the court deadline. He suggested the children would be transferred to ICE custody at Port Isabel shortly before the deadline. But he signaled they'd ask a judge for more time.

Azar said about 100 of the separated children are younger than five and subject to the rapidly approaching July 10 deadline. Officials there say they know the locations of all the children — some were sent hundreds of miles away to shelters around the country operated by nonprofits that care for them until a parent or other sponsor is identified.

A judge has put off — at least until Monday — a ruling on a Trump administration request for more time to reunite the children under five with their parents.

The Associated Press contributed to this report.