WASHINGTON  Senator Kirsten E. Gillibrand said Saturday that she and other sponsors of a stalled 9/11 health bill had won new Republican support for the measure and intended to try again to pass it before the end of the 111th Congress.

Following the Senate’s vote to repeal the ban on gays serving in the military, Ms. Gillibrand, Democrat of New York, said Democrats intended to resurrect the health initiative in the coming days after falling three votes short of breaking a filibuster against it earlier this month.

“We have the votes we need,” Ms. Gillibrand said. “We have indications from several Republicans that they very much want to vote for this bill.”

The $7.4 billion measure is intended to provide medical care to workers and others who had become ill as a result of being exposed to toxic debris and fumes at the site of the World Trade Center attack in 2001.