Republicans are pushing legislation to crack down on voting by noncitizens, which happens rarely and is already illegal in federal elections, in a move that reinforces former President Donald J. Trump’s efforts to delegitimize the 2024 results if he loses.

This week, House Republicans plan to vote on 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 they 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.”