In late July, a group of Republican activists met on a Zoom call to discuss preparations for the November election. The topic was how to keep undocumented immigrants from voting in November, a problem they claim, inaccurately, to be a looming threat to a fair election.

One woman, a local party chair from Georgia, recommended scouring school enrollment figures to find neighborhoods with large numbers of migrants. Another, Darlene Hennessy, an activist from the Detroit area, recommended hanging up signs in “ethnic” neighborhoods warning people not to vote if they were not eligible. She also suggested searching voter rolls for certain types of surnames.

“I think it’s unfortunate, but sometimes the only way you can find out is to look for ethnic names,” Ms. Hennessy said, according to a recording of the call obtained by The New York Times.

“We don’t want to be doing anything illegal,” she added.

There is no indication that noncitizens are voting in large numbers. And yet the notion that they will flood the polls — and vote overwhelmingly for Democrats — is animating a sprawling network of Republicans who mobilized around former President Donald J. Trump’s false claims of a rigged election in 2020 and are now preparing for the next one.

Activists like Ms. Hennessy, prominent lawyers, Republican lawmakers, right-wing influencers and other allies of Mr. Trump have ramped up pressure on local election officials to take steps that they say will keep noncitizens from tilting the election in Democrats’ favor. They have pressed for voter roll purges, filed lawsuits, prepared for on-the-ground monitoring of polling places and spread misinformation online.

Republican elected officials have responded. In Texas, the state’s Republican attorney general, Ken Paxton, recently announced an investigation into whether organizations were purposely registering noncitizens to vote. (He also authorized the state police to search the homes of activists who had been registering Latino voters as part of an investigation into allegations of voter fraud.) In Alabama, the secretary of state recently deactivated the registrations of more than 3,000 people, including some who are naturalized citizens, according to news reports, forcing them to update their records before they can vote.