The two sides are due in court Monday.
Lee Gelernt, an attorney for the American Civil Liberties Union, which brought the case, said he did not think the government was complying with the reunification order.
Only two children have been reunited with their parents since the government provided a list over the weekend of 102 kids under 5 in custody after being taken from their parents. The deadline is July 26. "I'm optimistic that many of these families will be reunited tomorrow".
"There are then some groups for whom the reunification process is more hard", lawyer Sarah Fabian told the judge.
He said that the reunification needed to occur within the next 14 days.
The 54 children set for reunification on Tuesday, along with five others awaiting final approval, will join their parents in Immigration and Customs Enforcement custody and then be released as a family, said Fabian, the government attorney.
It's been more than a week since they released a tally of how many kids from separated families remain in government custody. While parents were prosecuted, children were placed in the custody of the Health and Human Services Department in facilities dotted across the country.
In the case of 19 others, the parents have been released and their whereabouts is unknown, government lawyers said.
The American Civil Liberties Union received the list of the names of the almost 100 children under the age of 5 who were separated from their parents at the border, according to a group spokesman.
"It doesn't make sense", Gelernt said. "You've taken a child from a parent". "The children, some as young as 2 months old, can not possibly give permission for this", she added. The separations were in place from early May until Trump stopped the practice last month in the face of intense criticism.
"It may well be that once the plaintiffs know what the reason is and what groups [of parents] it applies to, they'll agree that a more relaxed date can apply to a certain group", Sabraw said at the conclusion of a lengthy conference.
In the court filing, the Justice Department sought clarification on whether they have to reunite migrant kids with parents who were already deported and appeared to argue that would be too hard and time consuming. This had shortened the period for confirmations to a few days from a couple of weeks.
Immigrant children under 5 will be returned to their families. In one account, a 14-month-old baby fleeing El Salvador past year was separated from his father at a port of entry in Southern California.
But DNA testing would, in theory, speed it up dramatically.
The child, identified only as "M.", now cries inconsolably and is afraid to be alone. Authorities say they are conducting DNA testing and background checks to protect children as required by a bipartisan anti-trafficking law enacted in 2008. Most will be released in the United States after being reunited with their children, Fabian said.