WASHINGTON — With new momentum on Capitol Hill for gun-violence-prevention measures, Sens. Chris Murphy and Richard Blumenthal unveiled a proposal Wednesday to extend gun-purchase background checks to sales of ammunition.

The Democratic-controlled House has approved bills to expand background checks to most private firearms transactions as well as lengthening the time limit on FBI employees who conduct the checks.

But the Senate remains in Republican hands, and Senate Majority Leader Mitch McConnell, R-Ky., is said to be unlikely to bring up gun legislation that would force potentially controversial votes by Republicans seeking re-election in 2020.

But the political calculations were absent as Connecticut Democrats Blumenthal and Murphy joined the parent of a victim of last year’s Parkland, Fla., shooting in unveiling the ammunition bill. Connecticut already requires background checks for ammunition purchases. 

Background checks on both guns and ammo “go hand in hand,” said Blumenthal. “All the same reasons (that apply to gun-buyer background checks) should apply to ammunition.”

The bill is called “Jamie’s Law,” after Jamie Guttenberg, one of 17 killed in the shooting at Parkland’s Marjory Stoneman Douglas High School a year ago.

Her father, Fred Guttenberg, was at the news conference Wednesday to support the bill.

“I don’t belong here,” said Guttenberg, who has become a gun-violence-prevention advocate since the shooting. “This isn’t what my life was supposed to be.”

Murphy said that Connecticut had seen a 40 percent reduction in gun homicides after the legislature adopted state-required background checks and a host of other gun laws in the wake of the Sandy Hook Elementary School mass shooting on Dec. 14, 2012.

The computerized checks on average take just a few minutes, he said. Legal gun owners pass them easily, while those not qualified to own guns under the law mostly cannot, he added.

“Don’t let anyone tell you we are going to create impediments to legal gun owners buying ammunition,” Murphy said.

The ammunition bill is just one item on a laundry list of measures that Democrats are pushing for — a strategy to channel new-found power in the House into an offensive on new gun laws after years of seeing Republican majorities in both House and Senate give them short shrift.

Other measures include a “Red-flag” statute, similar to the one Connecticut has had on the books since 1999. Under that law, family members and friends of troubled individuals can petition judges to have guns removed temporarily during acute phases when such persons are a danger to themselves and others.

On Thursday, Blumenthal and Murphy will join with Rep. Jahana Hayes, D-Conn., to present another bill.

It bars the U.S. Department of Education from using federal funds for the purpose of arming teachers. President Donald Trump and Education Secretary Betsy DeVos have advocated for arming teachers as a way of preventing mass shootings in schools.