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Story highlights

California Democratic Rep. Mike Thompson has filed a "discharge petition" to force a vote banning gun sales to people on no-fly list

House Speaker Paul Ryan says the idea suggested by President Barack Obama in his prime-time speech Sunday is a "distraction"

(CNN) —  

California Rep. Mike Thompson, the chairman of the House Democrats’ gun violence task force, is trying to force House Republican leaders to bring up a bill that would ban gun sales to those on the no-fly list. But Speaker Paul Ryan is already downplaying the possibility of a vote on the issue.

Thompson filed a “discharge petition” on the House floor Monday, and if he gets a majority of House members to sign it that procedural tool automatically brings the legislation up for a vote.

“If you agree that terrorists shouldn’t be able to have guns, then put your name down in writing and let’s have a vote,” Thompson said on the House floor.

But Republicans have already dismissed moving forward with that legislation, which President Barack Obama called for during a prime-time speech on Sunday.

RELATED: No-fly nightmares: The program’s most embarassing mistakes

Ryan, in remarks on Monday to the Wisconsin State Journal, called the President’s call for action on legislation addressing the no fly list “a distraction.”

“A mid-level bureaucrat can put anybody on a no-fly list with no due process rights,” Ryan said, according to the newspaper.

House Democrats are holding a mock hearing on the issue on Capitol Hill on Tuesday, to show their effort to respond to last week’s shooting in California and the terror attacks in Paris last month.

Discharge petitions rarely succeed in forcing a House vote. House leaders consider it a major break of party loyalty, although Democrats did score a rare victory recently by compelling a vote to resurrect the Export-Import Bank, legislation a swath of Republicans signed onto in support.

RELATED: Paul Ryan walks a tightrope as shutdown deadline nears