Those figures suggest the city may be close to resolving a painful legal battle with construction workers, police officers and firefighters who developed respiratory problems and other illnesses after working in the sooty ruins after Sept. 11, 2001.
The settlement, worth as much as $713 million, requires that 95 percent of the plaintiffs sign on by Nov. 8.
Mayor Michael Bloomberg implored workers again Tuesday to take the settlement, saying they would avoid a drawn-out fight while guaranteeing themselves at least some compensation.
"We have no desire to be fighting in court with those who acted unselfishly and heroically in their response to that attack, both on 9/11 and in its aftermath," Bloomberg told reporters in a news conference at City Hall.
Since the spring, the thousands suing over the lack of proper masks and other protections at the disaster site have been deciding whether to take a deal that would pay them a few thousand dollars to more than $1 million, depending on the severity of their illness and the likelihood it is connected to the dust.
Lawyers on both sides of the case have been campaigning hard for several months to hit the 95 percent target.
Paul Napoli, who leads a legal partnership representing the bulk of the workers involved in the suit, told The Associated Press that 75 percent of his clients had already signed on, and that if he counted those who have said they intend to opt in but haven't yet completed the paperwork, the acceptance rate tops 90 percent.
Bloomberg and the special master of the now-expired federal 9/11 victim compensation fund, Kenneth Feinberg, urged the workers Tuesday not to miss the deadline.
Their appeal was echoed at the news conference by Jean Marie DeBiase, whose husband, Mark, a phone technician from Jackson, N.J., was killed by lung disease in 2006.
DeBiase said her husband was exposed to trade center dust while setting up communications equipment at the city's disposal site on Staten Island. He suddenly fell ill four years later.
"It will bring closure to everyone involved," she said of the legal settlement. "No amount of money can bring my husband back, but it will enable my family, and others, to have some peace and try to go on with their lives."
At a hearing later Tuesday in federal court in Manhattan, a judge overseeing the settlement advised Napoli and other plaintiff lawyers to reach out again to holdout clients.
U.S. District Judge Alvin Hellerstein said the message should be, "This is a fair deal."
The judge also urged the lawyers to continue their efforts to expand the deal to cover additional defendants who have yet to settle, including some private contractors and the Port Authority of New York and New Jersey, which owned the trade center.
Congress is also considering legislation that would provide billions of dollars' worth of free health care and compensation payments to the workers.
The U.S. House passed a version of the bill last week. Similar legislation is pending in the Senate. Its prospects are uncertain.
Some ground zero workers had been reluctant to settle their legal claims against the city out of fear that doing so would disqualify them from any future federal compensation plan.
As currently written, only workers who reject the legal settlement and insist on taking their claims to court would be barred from participating in a federal aid program.