SAN DIEGO -- Lawyers for the Justice Department said in a court filing Tuesday that the federal government will miss a court-imposed deadline to reunite most of 102 migrant children under the age of 5 with their parents from whom they were separated. More children were reunited with their families Tuesday, but there were still dozens still separated from their families by the end of the day.

CBS News correspondent Mireya Villarreal reports that the judge wants to see constant progress and that there is a system in place that tracks these children.

As of Tuesday morning, four children had been reunited with their parents, according to the joint filing submitted by the government and the ACLU to the U.S. District Court for the Southern District of California.

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A June 26 court order stemming from a lawsuit filed over the Justice Department's "zero tolerance" policy -- which led adults and children to be separated when apprehended crossing the border -- gave the government two weeks to reunite children under the age of 5 with their parents, and one month for all others.

On a conference call with reporters Tuesday, Chris Meekins, chief of staff for the U.S. Department of Health and Human Services' assistant secretary for preparedness and response, said the administration has tried to speed up reunifications by adding extra staff to conduct criminal background checks and determine claims of parentage.

"Let me be clear, HHS could have transferred every child in HHS care to a parent if we did not take into account child safety," Meekins said.

Meekins said at least 14 children will not be reunited with those claiming to be parents, eight of whom failed criminal background checks, five of whom were determined not to be parents and one of whom is the subject of a claim of child abuse deemed to be credible.

The filing noted 13 others currently deemed ineligible for reunification, for reasons ranging from parents currently in the custody of other criminal justice agencies to a parent who is being treated for a communicable disease, and one who lives in a home with another adult who has a criminal background.

One child whose parents' location is unknown may not actually be an immigrant, according to the filing.

"Records show the parent and child might be U.S. citizens," lawyers for the government wrote in the filing.

Abril Valdes, an attorney with the American Civil Liberties Union of Michigan told the Associated Press that two young boys and a girl were among those reunited Tuesday with their families at a U.S. Immigration and Customs Enforcement facility in Grand Rapids, Michigan. The parents will be free while their cases wind through immigration court, and they're expected to be required to wear ankle monitors, AP reports.

Valdes says her client, Ever Reyes Mejia, and the other two fathers "were hugging and loving their" children and telling the kids that "they were never going to be separated again."

In total, the administration said it expects to ultimately reunite 75 of the 102 children with their parents. It noted that 20 of those parents were already deported, even though their children remain in U.S. government custody.

In the filing, the ACLU criticized the government's work reuniting the children with their parents.

"For (the parents) who were deported without their children, (government officials) have not even tried to contact them or facilitate their reunification by today," ACLU lawyers wrote.

There are as many as 2,900 more children five or older who remain in federal custody awaiting a July 26 reunification deadline, HHS Secretary Alex Azar said Thursday.