House Speaker Paul D. Ryan (R-Wis.) speaks during a news conference on Capitol Hill. (Pablo Martinez Monsivais/AP)

Nineteen House Republicans are pressing Speaker Paul D. Ryan to schedule a vote next week on legislation that would boost the national background check system for gun purchases.

In a letter led by Rep. Leonard Lance (N.J.), the lawmakers said the deadly mass shooting at a Florida high school last week has revived the push to overhaul the nation’s gun laws. They said passing the bill would be an “important step toward making our country safer from gun violence.”

The bill, which is narrow in focus, would reinforce the requirement that federal agencies report all criminal infractions to the National Instant Criminal Background Check System and create financial incentives for states to do so as well.

Sens. John Cornyn (R-Tex.) and Chris Murphy (D-Conn.) have introduced the bill, and earlier this month, President Trump signaled his support.

The House GOP lawmakers said the bill “would greatly improve the sharing of mental health and criminal record information between state and local agencies and the federal background check database. It has broad bipartisan support in both the House and Senate.”

Last year, the House passed the bill but only after coupling it with a measure allowing gun owners to carry concealed weapons across state lines, which Senate Democrats labeled a nonstarter.

Meanwhile more than 100 House Democrats plan to co-sponsor a bill banning assault weapons when Congress comes back in session next week, according to an email being circulated among members of the caucus.

Congress let the assault weapons ban passed in 1994 expire in 2004 and has not renewed it since. Rep. David N. Cicilline (D-R.I.), a co-sponsor of the bill, said Democrats should get behind outlawing “the sale, transfer, manufacture, or importation” of semiautomatic weapons capable of accepting more than 10 rounds of ammunition.

“They are weapons of war and they have no place in our community,” Cicilline wrote in an email to his colleagues, citing the massacre in Parkland, Fla.

A ban has the endorsements of several of the party’s top leaders, including Minority Whip Steny H. Hoyer (D-Md.) and Caucus Chairman Joseph Crowley (D-N.Y.) but not House Minority Leader Nancy Pelosi (D-Calif.), who has not commented on it since the shooting but tapped Rep. Ted Deutch (D-Fla.) to deliver a response, in which he called for the measure. The proposal in all likelihood is dead on arrival because Republicans control Congress and have not expressed support for it.