The announcement about the bill came days after the tragic shooting massacre in Las Vegas, Nevada.
"That bill is not scheduled now," House Speaker Paul Ryan told reporters, referring to a measure that also includes language making it more difficult to classify certain ammunition as "armor piercing."
"I don't know when it's going to be scheduled," Ryan added. "Right now we're focused on passing our budget."
The Sportsmen's Heritage and Recreational Enhancement Act advanced through a key House committee in mid-September, setting up a possible floor vote.
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The devices, also known as suppressors, do not eliminate gunshot noise entirely.
One of the bill's sponsors Republican Jeff Duncan, argues that reducing gun noise is a safety issue for hunters.
Trump, who said he will visit Las Vegas tomorrow, signalled that a debate about gun control might be coming.
"We'll be talking about gun laws as time goes on," he said.
Democrat Hillary Clinton, whom Trump defeated in the 2016 election, was among those expressing concern about easing access to silencers.
"The crowd fled at the sound of gunshots," Clinton tweeted yesterday. "Imagine the deaths if the shooter had a silencer."
Debate on the measure stalled after number three House Republican Steve Scalise was gravely injured in June at a congressional charity baseball practice.
Scalise returned to Congress last week to standing ovations, and today he briefly addressed the Las Vegas tragedy.
Ryan also spoke out against the "horror" of the shooting but stressed that "we can not let the actions of a single person define us as a country.
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