The U.S. government must reunite more than 60 children under the age of five who were separated by immigration officials after crossing into the United States from Mexico as soon as Tuesday or face penalties, a federal judge said.

U.S. Judge Dana Sabraw in San Diego told government attorneys he was sticking with deadlines he set last month, when he ordered children under five to be reunited Tuesday and another 2,000 to be back with their parents by July 26.

"These are firm deadlines. They are not aspirational goals," said the judge.

The children were taken from their parents under President Donald Trump's "zero-tolerance" immigration policy, which called for the prosecution and detention of adult immigrants crossing the border without authorization.

Sabraw also asked the American Civil Liberties Union, which brought the lawsuit that led to Sabraw's June order, to file papers on Thursday suggesting remedies if the government had not reunified the remaining children by Tuesday "or within immediate proximity of today."

After public outcry and a court challenge, Trump stopped separating families last month. The government had asked Sabraw to extend the deadlines because it needed time to test DNA to confirm family relationships, run background checks, locate parents who were released from custody and review parental fitness.

Sabraw's order included exceptions that might threaten the safety of the child. As a result, the number of children eligible to be reunited has shifted in recent days as the government has discovered some individuals were not parents as they claimed or had criminal records.

Health and Human Services Secretary Alex Azar told CNN's Wolf Blitzer on Tuesday that by the end of the day, he expects 38 children will have been reunited with their parents. Azar said for another 16 of the 102 migrants under five, the children weren't being reunited because the parents were found to either be "demonstrably unfit" or not to be the parents of the child in question.

For the remaining children, he said in about half of the cases, the government was still trying to finalize background checks and confirm parentage. In the other half, he said the parents weren't available to be reunited with their kids — in several cases because the parents were still in jail or U.S. Marshal Service custody.

In court filings, the ACLU has said the government is asking for needless provisions for reuniting families that would not happen if the families had not been separated in the first place.

The civil liberties organization said in a statement Tuesday night that "while the government is now attempting to comply with the court orders, it's failing because of real logistical problems, like missing records or parents whose locations it failed to track.

"But it is also stalling by insisting on sticking to status quo agency procedures in the face of extraordinarily unique circumstances."

Many of the separated children are fleeing violence in Guatemala, Honduras and El Salvador, and U.S. Homeland Security Secretary Kirstjen Nielsen met with diplomats from those countries in Guatemala on Tuesday to discuss U.S. immigration policies.

Some lawyers representing the separated children, who have been scattered into foster systems across the country, said the government was not telling them what would happen to their young clients. The Legal Aid Society in New York said it is representing at least two separated children under five years old that meet the judge's criteria for reunification on Tuesday.

One boy, from El Salvador, was due to be released to his mother, according to Beth Krause, the supervising attorney of Legal Aid's Immigrant Youth Project. "I have no details about where, when, under what conditions," she wrote in an email on Tuesday morning.

The other boy, a Honduran, would remain with a foster family while the father remained in government custody, although it was not clear to her why. "I know very very little about this case," she said. "It's all very frustrating."

Sabraw issued a protective order shielding children's names and some reunification details from disclosure.

Trump was dismissive of reporters' questions about the missed deadline on Tuesday. "Tell people not to come to our country illegally," he said. "That's the solution." Some of the separated families arrived at U.S. ports of entry seeking asylum, which is not illegal.