Several of Paul Weiss’s top clients declined to comment. A spokesman for Citigroup, Edward Skyler, said jokingly, “Given how valuable their time is, which we can attest to, it’s very admirable.”

Paul Weiss, among the firms known to lean left, has a reputation for public interest work, including the 2013 Supreme Court case that legalized gay marriage. Brad S. Karp, its chairman since 2008, has recently emerged as an outspoken leader. Thirty-four firms signed onto an op-ed he wrote with Mr. Wingens in The New York Times this summer denouncing family separations.

To date, Paul Weiss lawyers have spent more than $2 million in billable hours on the A.C.L.U. project, the firm said. Paul Weiss is not litigating the case but was appointed by the court to help the nonprofit find and represent deported parents. Jeh C. Johnson, the secretary of Homeland Security under Mr. Obama, is a partner at the firm but is not involved in the effort.

“We’re reuniting families destroyed by the administration,” Mr. Karp said in an interview.

Emily Goldberg, pro bono counsel at Paul Weiss, orchestrated the firm’s response to family separations.

In June, Ms. Goldberg received a list of about 175 separated children who had been sent to agencies in New York. Catholic Charities, the organization assigned to provide the children with legal representation, could not find their parents. Ms. Goldberg enlisted the help of lawyers at several major firms, and when they could not find a number of the parents, they concluded the parents had been deported. She contacted Dentons, an international firm with offices in Central America, and its employees started looking for parents there.

Weeks later, the government revealed the existence of the deported parents. The judge in the suit, Dana Sabraw, ordered the government to reunite these families but asked the A.C.L.U. to lead the effort. Lee Gelernt, deputy director of the A.C.L.U. national Immigrants’ Rights Project, turned to Paul Weiss, which became the head of a committee that would work with three nonprofits to find the parents, he said.

“I think we did quickly realize that this was going to be an enormous task,” Mr. Gelernt said. The parents were in Guatemala, Honduras, El Salvador, Mexico, Brazil and Romania.

