The House voted 402-12 to pass the "Never Forget the Heroes Act" that had been championed by Jon Stewart, the popular former host of the late-night comedy program The Daily Show, and highlighted by recent gripping testimony by a dying 9/11 New York police detective.
"On September 11th and its aftermath, our brave first responders were there for us. We must always be there for them," House Speaker Nancy Pelosi said just before the vote on the bill.
Senate Majority Leader Mitch McConnell said legislation will be brought to a vote in his chamber soon.
Without prompt action by Congress, victims of the attack would see steeply reduced benefits due to a lack of funding.
Former New York Detective Luis Alvarez died last month shortly after his testimony to the U.S. House Judiciary Committee in which he urged a replenishment of the fund.
At that same hearing, Stewart delivered impassioned testimony in which he chastised some lawmakers for not acting quickly enough to continue helping the police, firefighters and other workers immediately following the Sept. 11 attack.
If passed by the Senate and signed into law by President Donald Trump, the victims' fund would be authorized through 2092 and they could file claims until October 2089.
It would end the string of temporary measures that have required constant lobbying by groups trying to avert an interruption in benefits to help those sickened by toxic materials released into the atmosphere and ground following the impact of commercial jetliners that were hijacked and flown directly into the twin towers.
Government officials told responders at the time that it was safe to work at the site, despite questions by many experts.