More than 30 lawmakers in both parties back the bill, as does Sandy Hook Promise, a group formed by parents of the children killed in the 2012 Sandy Hook Elementary School shooting in Connecticut. A similar bill by Senator Orrin Hatch, R, is awaiting consideration in the Senate.
The bill reauthorises a programme created in 2001 through the Justice Department to prevent threats against schools. The legislation authorises US$50 million to intensify school security, pay for federal "threat assessment teams" to help school districts sort through reported threats, create an anonymous reporting system so that students and others can report threats and pay for training and technical assistance programmes for law enforcement and school officials to help identify potentially violent behaviour.
But the bill says nothing about firearms - a top demand of the Stoneham Douglas students, who sparked the national walkout and ongoing campaign to enact gun control measures.
Students at the high school are pushing for consideration of a proposed federal ban on military-style rifles and a revamp of the national criminal background check system that failed to pass five years ago in the wake of the Sandy Hook shooting.
"There is still much work to be done, but the best way to keep our students and teachers safe is to give them the tools and the training to recognise the warning signs to prevent violence from ever entering our school grounds. This bill aims to do just that," Rutherford told reporters.
House Majority Leader Kevin McCarthy, R, added at a weekly GOP news conference that Rutherford's bill "will not be the only bill" passed to address school violence.
McCarthy noted that the House late last year passed legislation that would bolster the background check system by compelling federal agencies to accurately and quickly report information about people banned from banning weapons. But the "Fix NICS" proposal was coupled with a bill that would greatly expand the ability of Americans to carry concealed weapons across state lines.
A similar "Fix NICS" proposal awaits consideration in the Senate, but it is being held up by Republicans opposed to potential curbs on due process rights and Democrats pushing for a broader debate on gun control.
Senate Minority Leader Charles Schumer, D, decried the lack of broader congressional action to prevent deadly school shootings, comparing the scourge of gun violence to drug addiction and incurable diseases.
"Why is it that when it comes to gun violence, which is responsible for just as many if not more deaths, we throw up our hands, we pretend there is no solution?" Schumer asked.
Similar sentiments expressed by several Democrats earned applause from the audience at the Judiciary hearing.
"I don't know what we are waiting for," said Senator Kamala Harris, D. "We don't need any more tragedies, and we don't need any more new ideas. We've got great ideas. What we need is the courage for Congress to act."