Republicans are using their majority in Congress to reinforce former President Donald J. Trump’s false claims of widespread illegal voting by noncitizens, sowing the seeds of an effort to delegitimize the outcome of the 2024 election if Mr. Trump loses by pushing legislation that purports to crack down on a problem that barely exists.

House Republicans have introduced a series of bills to take aim at voting by noncitizens, which is already a felony in federal elections, where those who study the issue say it almost never occurs.

On Wednesday, they are planning to push through a bill that would roll back a District of Columbia law allowing noncitizens to vote in local elections, which they contend is needed to prevent Democrats from expanding the practice to other jurisdictions. And Republicans are advancing another measure that would require states to obtain proof of citizenship, such as a birth certificate or passport, when registering a person to vote.

The legislation has virtually no chance of becoming law, but it serves to amplify one of Mr. Trump’s favorite pre-emptive claims of election fraud. It also underscores Republicans’ embrace of a groundless narrative — one that echoes the racist “great replacement” conspiracy theory — that Democrats are intentionally allowing migrants to stream into the United States illegally in order to dilute the voting power of American citizens and lock in electoral victories for themselves.

Speaker Mike Johnson recently appeared alongside Mr. Trump at Mar-a-Lago, the former president’s Florida resort and residence, to announce a pledge to get tough on migrants flowing across the border, suggesting with no evidence that they were coming in unchecked as part of a plot to vote for President Biden.

“There is currently an unprecedented and a clear and present danger to the integrity of our election system — and that is the threat of noncitizens and illegal aliens voting in our elections,” Mr. Johnson warned during a news conference on the steps of the Capitol this month.

But he conceded that he had no evidence to support that assertion.

“We all know, intuitively, that a lot of illegals are voting in federal elections, but it’s not been something that is easily provable,” Mr. Johnson said. “We don’t have that number.”

In fact, estimates are known and they are exceedingly low; a nationwide survey found the number of noncitizens suspected to have voted in the 2016 election was about 30.

“They don’t ever bring any evidence of actual fraudulent efforts being made by non-U.S. citizens to vote in federal elections,” said Representative Joseph D. Morelle of New York, the top Democrat on the Administration Committee. “So I think it’s pretty clear, pretty quickly, that this is all a pretext. They’re going to, once again, challenge the results of the election and they need to have a reason.”

Fears of noncitizens voting in American elections date back to the 1800s, but they have reached a fever pitch during the Trump era. Shortly after taking office in 2017, Mr. Trump met with congressional leaders at the White House and falsely claimed that he would have won the popular vote over former Secretary of State Hillary Clinton but for the three million to five million illegal immigrants who voted for her.

After Mr. Trump lost the 2020 election, there was so little evidence of noncitizens voting that he and his allies largely avoided the topic as they pushed to overturn the election results. They instead made myriad other complaints, including the use of drop boxes and mail-in voting during the coronavirus pandemic. They also pushed debunked conspiracy theories, including hacked voting machines, the dead voting en masse, and Italian satellites and Chinese-rigged thermostats flipping votes.

After falsely hyping the risk of illegal voting by noncitizens in previous elections, Republicans say this time is different. They maintain that so many undocumented immigrants have crossed into the country that the likelihood has grown, and that even a minuscule amount of illegal votes could swing a presidential election.

The bill slated for a vote on Wednesday, sponsored by Representative August Pfluger, Republican of Texas, would repeal a D.C. law enacted in 2022 that allows noncitizens to vote in local elections. A number of municipalities, including towns in Maryland and California, allow noncitizens to participate in local elections, particularly for school board, where their children go to school.

Representative Bryan Steil, Republican of Wisconsin and chairman of the Administration Committee, warned at a recent hearing that the practice could spread. He pointed to a programming glitch in Pennsylvania that allowed noncitizens to register to vote and a review that found more than 100 noncitizens on Ohio voter rolls.

“American elections are for American citizens, and we intend to keep it that way,” Mr. Steil said.

Representative Eleanor Holmes Norton, the Democrat who is D.C.’s nonvoting delegate, argues that Congress has no business interfering in D.C.’s local affairs.

Republicans also are moving forward this week on the Safeguard American Voter Eligibility Act, sponsored by Representative Chip Roy, Republican of Texas and an influential leader of the ultraconservative House Freedom Caucus.

Mr. Roy’s bill would require states to obtain proof of citizenship, such as a birth certificate or passport, in person when registering someone to vote and require states to remove noncitizens from voter rolls.

“Secure elections are a key cornerstone for any representative government; without them, we won’t have a country,” Mr. Roy said in a statement. “Radical progressive Democrats know this and are using open border policies while also attacking election integrity laws to fundamentally remake America.”

Democrats contend that requiring voters to register in person and produce a birth certificate or passport — which many Americans, particularly teenagers or younger adults, do not have readily available — simply makes it harder for citizens to vote.

Nearly 40 percent of the adult voting population did not cast a ballot in the last presidential election, and Mr. Morelle argued that further roadblocks would only make it more difficult for Americans to participate.

“It’s just another way of stopping people from voting,” Mr. Morelle said of the G.O.P. legislation. “I mean, they just continue to suppress the ability of people to vote.”

Brad Raffensperger, the Georgia secretary of state who famously rejected Mr. Trump’s demands to overturn the results of the 2020 election in his state, has found common ground with Mr. Trump and Mr. Johnson over banning noncitizens from voting.

“Since I took office in 2019, I’ve urged Congress to take action to change federal law and ensure that noncitizens cannot vote in our elections,” he said in a statement. “I thank Speaker Johnson and the former president for following my lead, and I look forward to action finally being taken in Congress.”

But David Becker, the director of the Center for Election Innovation & Research, said that cases of noncitizens voting in federal elections were very rare and that he suspected that Republicans had ulterior motives.

“Imagine someone who had risked everything to be in the United States, or had gone through all of the process to be here legally, risking their status by shining a hot spotlight on themselves and a bull’s-eye on themselves in order to cast one ballot in an election in which 160 million ballots are going to be cast,” he said. “It doesn’t happen.”

Mr. Becker said the federal government and states, including Georgia, already had good policies in place to prevent it.

“This is largely being done, along with other lines of disinformation, to prep the United States for the argument that an election was stolen by people who apparently believe the candidate they support is likely to lose,” Mr. Becker said.