The number of migrant parents who have signed away the right to be reunited with their children is significantly lower than the Trump administration has said before, according to fresh information the government filed in a family-separation court case.

The latest figures show that 34 parents waived the chance to be back together with their children — compared with the 120 that the government reported a week earlier. Migrants’ advocates and congressional Democrats have challenged the idea that large numbers of parents were signing away those rights, contending that some — traumatized by the separations — were misled, did not understand the form or never signed in the first place.

The data, filed in federal court late Thursday, shows a modest increase in the number of youngsters returned to their parents after being separated at the southern U.S. border. But at a court hearing Friday, U.S. District Judge Dana M. Sabraw noted that the government has made little headway in locating — let alone reuniting — the parents of more than 400 children in families in which the adult has been deported or has returned on their own to their home country, mainly Guatemala or Honduras.

Sabraw, a Republican appointee, chided the government for trying to shift responsibility for tracking down the remaining separated parents to the American Civil Liberties Union, which filed the lawsuit that led him to issue the reunification order.

The government had proposed leaving it mainly to the ACLU and its allies to find the rest of the parents, including those who have been deported or whose whereabouts in this country are unknown, and verify whether they want their children back.

“The reality is, for every parent who is not located, there will be a permanently orphaned child, and that is 100 percent the responsibility of the administration,” Sabraw said.

He told lawyers that “it was disappointing” the government had not yet given him a plan for finding and reuniting the remaining families. And he directed the administration to put one federal official in charge and report how the work will be carried out.

In Thursday’s court filing, the ACLU had pushed back against the Justice Department proposal, saying that the group and its allies “will do whatever they can to help locate the deported parents, but emphasize that the government must bear the ultimate burden of finding the parents.”

“Not only was it the government’s unconstitutional separation practice that led to this crisis,” the ACLU wrote, “but the United States government has far more resources” than nonprofit groups or outside law firms.

The court filings showed that, of 2,551 children ages 5 to 17 who were separated, 1,979 have been released from shelters overseen by the Department of Health and Human Services’ refu­gee office — nearly 160 more than a week earlier. Most were reunited with their parents, though some were placed with other relatives or other responsible adults, or had turned 18 themselves.

Hundreds of the reunified families are in custody in family detention centers run by Immigration and Customs Enforcement, while hundreds more have been released to await immigration proceedings.

The number of children whose parents are presumably still in the country, but whose whereabouts are unknown to the government, declined sharply in the past week — from 94 to 15, according the data, which covered through midday Wednesday.

Late last year, the Trump administration increased separations of children and parents, many of whom were fleeing violence and other harsh conditions in their countries. Officials believed that splitting up families would deter border crossings.

In May, Attorney General Jeff Sessions announced a “zero tolerance” policy in which all adults crossing the border would be jailed and prosecuted, with their children taken away and placed in shelters for migrant youths.

Following a bipartisan outcry, President Trump halted the separations. But federal agencies were ill prepared to return children to their parents.

The court filing does not explain why the number of parents waiving the right to be reunited has plummeted. HHS officials have said they continue to ask parents in immigration custody whether they want their children back and that, if any change their minds, they are being reunited.

At a hearing this week before the Senate Judiciary Committee, Matthew Albence, a senior ICE official, sidestepped questions about whether every parent who had left the country without a child had signed a waiver.

“Is there documentation for what you claim?” asked Sen. Richard J. Durbin (D-Ill.).

“Right now, the form that we’re utilizing . . . is an ACLU-developed form, approved by the court,” Albence replied.

“I know you can get to a yes or no,” Durbin countered, “and that’s what I’m looking for.”

Albence repeated his answer.

Cmdr. Jonathan White, the public-health official who has led the reunification effort for HHS, told the senators that, while signing away reunification rights may be difficult to fathom, “many parents have made this journey to deliver their children here because that is the desperate, last act of a parent trying to take the child out of some of the most dangerous places to raise a child in the world.”

Maria Sacchetti contributed to this report.