A bipartisan group of House Intelligence Committee members have introduced a companion bill to the Senate’s Secure Elections Act, which aims to significantly bolster America’s digital voting election infrastructure against future cyberattacks.

The proposal was offered on Friday by Reps. Tom Rooney, Florida Republican, Trey Gowdy, South Carolina Republican; Jim Himes, Connecticut Democrat; and Terri Sewell, Alabama Democrat.

It addresses a host of election security issues and would provide grant funding for states to replace old, paperless voting machines. New systems would include a paper trail in case an election outcome is disputed and requires an audit.

“Although the Russian government didn’t change the outcome of the 2016 election, they certainly interfered with the intention of sowing discord and undermining Americans’ faith in our democratic process,” Mr.Rooney said in a statement on Friday. “There’s no doubt in my mind they will continue to meddle in our elections this year and in the future.”

The bill is the latest indication that recent Russian election meddling efforts continue casting a long shadow over Capitol Hill as states make final preparations for November’s general elections, with every House seat up for grabs, along with a third of the Senate and many state and local contests.

According to the Department of Homeland Security, in 2016 Russian hackers targeted election-related systems in 21 states and while no votes were changed, operatives were able to penetrate networks, including Illinois’ voter registration databank.

After that revelation surfaced, Washington lawmakers and state election officials were furious with DHS officials for taking so long to reveal what they knew about the cyberattacks.

“It is our responsibility to take every precaution necessary to safeguard our elections and ensure no vote count is ever interfered with,” Mr. Gowdy said in a statement.

On the other side of the Capitol, the bipartisan Senate Secure Elections Act has been pushed forward all year by Sen. James Lankford, Oklahoma Republican, and Sen. Amy Klobuchar, Minnesota Democrat, gaining support from the leaders of the Senate Intelligence Committee along the way.

The introduction of the House companion bill gives the issue significant momentum in Congress as the midterms rapidly approach.

Both proposals also aim to increase communications between federal and state agencies regarding potential threats.

Ms. Sewell noted that with less than 100 days until the midterms “action is urgently needed to protect our democracy against another attack.”

Congress has already taken steps to shore up voter-registration rolls, vote-tabulation systems and election procedures by allocating $380 million earlier this year for upgrades intended to prevent hacking.

According to the federal Election Assistance Commission, the agency overseeing the process, at least 24 states are now accessing the cash after agreeing to provide a 5 percent match and submitting spending plans.