Trump administration health chief Alex Azar said Thursday that no immigrant children separated from their parents have been reunited with their families in federal custody — yet — to comply with looming court order deadlines to do so.

But Azar said the U.S. Health and Human Services Department will comply with the first of those deadlines to take children in HHS custody and place them with parents who are in the custody of Immigration and Customs Enforcement next Tuesday.

Azar said there are somewhat fewer than 3,000 kids who were separated from their parents when they jointly tried to illegally cross the border with Mexico.

That is much higher than the 2,047 children that HHS recently said were in its custody. Azar said the new number is higher because a judge has required HHS to reunite all separated children, including ones taken from parents before the Trump administration's zero tolerance policy took effect in May.

"We have not [placed] children into ICE custody yet, but we will do so with the court's order and supervision," Azar said.

He said HHS is working "overtime" to confirm that the people who purportedly are parents of those children actually are their parents, and is also checking to see if any parents have a background that makes them dangerous to receive a child. Azar said that verification process in some cases involves DNA testing.

HHS has until Tuesday to reunite children up to the age of 4 with their parents in the custody of Immigration and Custom Enforcement, and a deadline of July 26 to reunite the remaining kids. He said 100 kids in HHS custody now are under the age of 5.

U.S. District Court Judge Dana Sabraw issued the deadlines last week.

"Yes, we will comply with the court's deadline," HHS Secretary Azar told reporters during a conference call. "We will do as much as possible up to the deadlines set by the court."

"We have a plan in place to get this job done while maintaining the safety of the children in our care," he said.

That plan includes transferring parents of separated children to custody facilities that are closer to the kids.

During the conference call, Azar several times blamed Congress and the courts for the controversy and confusion surrounding the policy of separating immigrant children from their parents after illegal border crossings.

When asked by a reporter if the administration could have avoided that controversy by preparing better for its new policy of family separation, Azar did not answer the question.

Instead, he noted that normally, "if you break our law ... you do not get to stay with your children."

"The simplest way to avoid that," Azar added, is by not trying to cross into the United States illegally.