After years of fighting in court, lawyers representing the city, construction companies and more than 10,000 ground zero rescue and recovery workers have agreed to a settlement that could pay up to $657.5 million to responders sickened by dust from the destroyed World Trade Center.

The settlement was announced Thursday evening by the WTC Captive Insurance Co., a special entity established to indemnify the city and its contractors against potential legal action as they moved to clean up the site after the Sept. 11, 2001, terror attacks.

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The deal, which still must be approved by a judge and the workers themselves, would make the city and other companies represented by the insurer liable for a minimum of $575 million, with more money available to the sick if certain conditions are met.

Most if not all of the money would come out of a $1 billion grant from the Federal Emergency Management Agency.

Mayor Michael Bloomberg called the settlement “a fair and reasonable resolution to a complex set of circumstances.”

“The resolution of the World Trade Center litigation will allow the first responders and workers to be compensated for injuries suffered following their work at Ground Zero,” he said in a statement.

Marc Bern, a senior partner with the law firm Worby, Groner, Edelman & Napoli, Bern LLP, which negotiated the deal, said it was “a good settlement.”

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“We are gratified that these heroic men and women who performed their duties without consideration of the health implications will finally receive just compensation for their pain and suffering, lost wages, medical and other expenses, as the U.S. Congress intended when it appropriated this money,” he said in a statement.

Workers who wish to participate in the settlement would need to prove they had been at the World Trade Center site or other facilities that handled debris. They also would have to turn over medical records and provide other information aimed at weeding out fraudulent or dubious claims.

For the settlement to be enforced, 95 percent of the workers would need to agree to be bound by its terms.

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The agreement comes with just two months to go until the first trials are to begin in the case. Thousands of police officers, firefighters and construction workers who put in time at the 16-acre site in lower Manhattan had filed lawsuits against the city, claiming it sent them to ground zero without proper protective equipment.

Many of those workers now claim to have fallen ill. A majority complained of a respiratory problem similar to asthma, but the suits also sought damages for hundreds of other types of ailments, including cancer.

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Lawyers for the city claimed it did its best to get respiratory equipment to everyone who needed it. They also had challenged some of the claims as based on the thinnest of medical evidence, noting that thousands of the people suing suffered from conditions common in the general population or from no illness at all.

Under the settlement, the task of deciding what each worker will be paid will fall to a neutral third party, to be picked by the two sides. Lawyers for the plaintiffs have previously said they favor Kenneth Feinberg, the special master who determined payouts from the federal fund set up to compensate victims of the terror attacks.

Payments will be based on a system that ranks each illness by severity and factors in potential exposure to the dust.

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Some workers are likely to receive payments of only a few thousand dollars. Others could be in line to get more than $1 million, depending on their injuries.

A special insurance fund will be set up to cover workers who develop cancer in the future.

Lawyer Andrew Carboy, who represented a group of firefighters in the case, said he would urge them to accept the deal.

“The proposed settlement demonstrates that the justice system can tackle such a factually complicated and emotionally charged situation,” he said. “The settlement, most importantly, will treat each worker as an individual. And their settlement will be based on the merits of their case.”

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Both sides in the case were scheduled to appear Friday afternoon before the federal judge handling the litigation, U.S. District Judge Alvin Hellerstein, who previously had said he favored a settlement but planned to analyze it carefully to make sure it was fair.

The settlement would mean a postponement or cancellation of the trials tentatively scheduled to begin in May. Some of the cases scheduled to be heard first included that of a firefighter who died of throat cancer and another who needed a lung transplant, as well as workers with less serious ailments, including a Consolidated Edison utility company employee with limited exposure to the debris pile and no current serious illness.

The $1 billion fund created by Congress to help insure the city has been depleted somewhat by the long legal battle in the case, with the bill so far running to more than $200 million.

The Worby, Groner, Edelman & Napoli, Bern law partnership, which represents 9,000 of the plaintiffs, is expected to take as much as a third or more of the total settlement in legal fees, based on contingency agreements it signed with each client.