Men and women who participated in the ground zero cleanup had until the end of the day Monday to decide whether to join a deal that would pay at least $625 million to people who developed illnesses after working in the rubble.
Related settlements could raise the total compensation for the workers to as much as $815 million.
The deal was struck in the spring, but it remains tentative. Under its terms, the settlement only takes effect if at least 95 percent of the workers agree to sign on.
A lawyer for about 9,000 of the workers, Paul Napoli, told The Associated Press last Friday that the plaintiffs were very close to hitting that target, but the final results may not be known for days.
U.S. District Judge Alvin Hellerstein, who has been overseeing the litigation, issued a gag order late Monday barring the attorneys involved in the case from talking to the media about how the tally had gone.
He wrote that he was doing so "to avoid confusion and speculation flowing from the dissemination of incomplete information."
In his order, he said a "huge influx of claims" in the final days before the deadline had taxed the system he and the lawyers had set up to handle the mountain of required paperwork.
Initially, all of the necessary documents were supposed to be uploaded to a court-authorized website by 11:59 p.m. Monday.
Hellerstein said he was extending that deadline until 3 p.m.
Thursday. The extension applies only to the processing of paperwork. It does not give the workers more time to decide whether they wish to join the settlement, he said.
Hellerstein asked the lawyers in the case to report the results to him first, and said he would release their findings on the court's Web site "promptly" once they do so.
More than 10,000 construction workers, police officers and firefighters have sued the city and a long list of companies over their handling of the cleanup of lower Manhattan after 9/11.
Medical studies have suggested that exposure to the dust may have led to respiratory problems for many of the workers. In the lawsuits, they have blamed city officials for sending people to the site without proper protective equipment.
It isn't clear what would happen if the 95 percent participation threshold wasn't met. The special insurance entity defending the city in the case could then declare the settlement dead, but nothing would prevent it from relaxing the requirement slightly if it wished.