(CNN) How many immigrant families have been reunited since a judge ordered the US government to halt most family separations at the border?

And how many kids from separated immigrant families are still in government custody?

We don't know, because officials aren't saying.

It's been more than a week since they released an exact tally of how many kids from separated families remain in government custody.

And officials have repeatedly declined to respond to questions about how many families have been reunited.

Deadlines are looming; the government has less than a month to reunite the families it separated. Here's the latest:

On June 20, the Department of Health and Human Services said there were 2,053 children from separated families in its care. On June 26 , the agency said there were 2,047 such children.

About 100 of those kids, he said, are under age 5.

Why is the new total estimate so much higher than previously released figures? And why won't officials release a new, precise tally?

According to Azar, it's because a court order required officials to go back further in time and comb through thousands of cases to find any separated children -- not just to focus on the administration's new "zero tolerance" policy, which officials announced in May

"We are starting with the largest potential data set that we have. We don't want to be under-inclusive," he said. "We are erring on the side of inclusion until we can rule any connection out."

how many kids from separated families remain in custody. Federal officials have released updated statements revealing the total number of immigrant children in their care -- a figure that includes children who crossed the border alone and children who were separated from their families after crossing. But since June 26, they've refused to specify exactlyhow many kids from separated families remain in custody.

Here's why that particular statistic matters: It's the only figure officials have provided that gives us any indication of whether reunions are happening.

This isn't a perfect equation; we don't know whether the children released from HHS custody were reunited with parents -- only that they're no longer in one of the agency's shelters. The government has not answered questions about the circumstances of their release.

But without a response to questions about how many reunions have occurred -- or at least an updated, precise figure on the number of kids from separated families who remain in custody -- the public has no way to track whether families are being reunited or how quickly it's occurring. All we have are anecdotal examples of a few scattered reunions at airports

Reuniting families separated under the Trump administration's hardline immigration policies will be no easy task. According to information a government official gave CNN, as of June 25 children from separated families were scattered in HHS Office of Refugee Resettlement shelters in 16 different US states.

Azar and other HHS officials said Thursday that DNA tests are being used as part of the reunification process.

The HHS program that handles immigrant children, he said, wasn't designed to track the circumstances that led up to them ending up in the agency's custody.

But Azar sought to shift blame from the administration that conceived and implemented these policies to Congress and the courts instead.

"While I know there has been talk of confusion, again, any confusion is due to a broken immigration system and court orders," he said.

"The Trump administration's attempt to shift the blame to the court is incomprehensible given how much time the court gave the government to fix its own mess," said Lee Gelernt, deputy director of the ACLU's immigrants' rights project. "When the government wants to marshal its resources to separate families, it has shown that it can do it quickly and efficiently, but when told to reunite families, it somehow finds it too difficult and cumbersome to accomplish."

By July 6, officials must make sure every separated parent has a way to contact their child. By July 10, children under 5 must be reunited with their parents. And by July 26, all children should be reunited with their parents.

Azar described the deadlines as "extreme," but said that officials would comply.

Officials are scheduled to appear in court on Friday for a status hearing.

Attorneys for the ACLU say they are monitoring the situation and will go back to the court if officials fail to comply with the deadlines.

Note: This story has been updated to reflect the latest information released by the Department of Health and Human Services.