By A. G. SULZBERGER and MIREYA NAVARRO

Lawyers for the city and some 10,000 rescue and cleanup workers at ground zero said Thursday that they had negotiated a new settlement that would give the workers more compensation for health damages and reduce the fees paid to their lawyers.

A federal judge rejected an earlier settlement in March as inadequate. After nearly three months of renegotiations, the city’s insurer, the WTC Captive Insurance Company, has agreed to increase its payout to plaintiffs to $712.5 million. The previous terms called for payouts of $575 million to $657.5 million.

The workers sued the city and its contractors six years ago over respiratory illnesses and other injuries they say they suffered at the World Trade Center site in the 9/11 recue and cleanup effort, arguing that they were not given protective equipment or adequate supervision.

On March 12, lawyers for the city and the plaintiffs reported that they had reached a settlement after arduous negotiations. But a week later, the judge overseeing the case, Alvin K. Hellerstein of United States District Court in Manhattan, startled both sides by spurning it.

He said the workers were getting too little, the terms were poorly understood by the plaintiffs, and the lawyers were receiving too big a cut. Under the new accord, the plaintiffs’ lawyers have agreed to reduce their fees to a maximum of 25 percent of the settlement amount, down from the 33.33 percent called for in agreements their clients had signed. As a result, the plaintiffs will get to keep an additional $50 million, their lawyers said.

Judge Hellerstein welcomed the new settlement in a hearing on Thursday morning. “This is a very good deal — I am very excited by this deal,” he said.

He acknowledged that his intervention in the class action settlement had been unusual but said that the gravity of the claims demanded it. “It just begs for judicial supervision, and I have exercised it, and I will continue to exercise it,” he said.

In March the city filed papers with the United States Court of Appeals for the Second Circuit to challenge Judge Hellerstein’s authority to block the settlement. But at the same time, its lawyers have sought to accommodate him to salvage the agreement.

The new settlement must be approved by 95 percent of the plaintiffs by Sept. 30 to take effect. At the hearing on Thursday, the judge urged the workers to accept it. “It is time to end this lawsuit,” he said.

Once approved, he said, the payments could start flowing to the plaintiffs within weeks.

Kenneth R. Feinberg, the former special master of the federal compensation fund that paid awards to families of 9/11 victims in a separate process, said, “This settlement brings to an end one of the final chapters of the 9/11 tragedy.”

He said he would visit fire houses and conduct town hall meetings to explain the new settlement to the workers.

Paul Napoli, a lawyer representing thousands of the firefighters, said the new deal “can be described in three words: bigger and better.”

Judge Hellerstein scheduled another hearing for June 23 at which plaintiffs can pose questions and voice concerns about the settlement terms.