Democrats in the House followed Senate colleagues on Friday in proposing legislation meant to safeguard future elections from foreign interference.

Introduced by Reps. Bennie Thompson of Mississippi, Zoe Lofgren of California and John Sarbanes of Maryland, the Election Security Act would require states to use paper ballots, establish federal cybersecurity standards for vendors of voting systems and allocate more than $1 billion toward securing and maintaining related infrastructure, among other measures.

“With the 2020 elections just 18 months away, we cannot afford to be complacent about the security of our elections. Nothing less than the integrity of our democracy is at stake,” said Mr. Thompson, the chairman of the House Committee on Homeland Security.

“Russia successfully attacked our elections in 2016 and it is clear they will try to again next year,” Mr. Thompson added. “Despite repeated warnings from well-respected national security officials the White House has failed to lead a whole-of-government effort to keep our adversaries out of our elections, so Congress will step up.”

Hackers working on behalf of the Russian government interfered in the 2016 presidential race in part by attempting to breach election infrastructure throughout the country, and the FBI has assessed that at least Florida county government was successfully compromised during the course of those campaigns, according to the redacted report released last month by Robert Mueller, the special counsel appointed to investigate Moscow’s involvement for the Department of Justice.

Election systems in all 50 states were targeted by Russian hackers in 2016, federal officials said previously, and the heads of both the FBI and Department of State recently said Moscow is expected to meddle again in 2020.

“With our intelligence agencies increasingly warning us about the impending foreign attacks on our elections in 2020, we must act quickly to shore up our defenses and protect our democracy,” Mr. Sarbanes said in a statement.

In addition to attacking election infrastructure, Mr. Mueller’s investigation found that Russia attempted to meddle in the race by using internet platforms to propagate false and misleading information, including through purchasing politically-charged ads seen by millions of Facebook users in the U.S.

A separate bill introduced Wednesday this week in the Senate, the Honest Ads Act, would require political ads sold online to follow the same transparency and disclosure rules as ones paid to be played on TV and radio if passed.

“Hardening our electoral infrastructure will require a comprehensive approach and it can’t be done with a single piece of legislation,” said Sen. Lindsey Graham, a South Carolina Republican who introduced that proposal with Democratic co-sponsors Mark Warner of Virginia and Amy Klobuchar of Minnesota.

Earlier versions of both the Election Security Act and Honest Ads Act failed in the House and Senate, respectively.

Sen. Ron Wyden, Oregon Democrat, said in March that planned to introduce a bill similar to the Election Security Act that would allocate hundreds of millions of dollars for states to purchase the machinery needed to count paper ballots if passed.