It has been nearly four years since a parade of judges dismissed wild claims from Donald J. Trump and his associates about hacked election machines and a year and a half since a leading machine company obtained a $787.5 million settlement from Fox News over the debunked conspiracy theories.
But Mr. Trump’s presidential campaign and his closest allies are again trotting out the theories as part of a late-campaign strategy to assert that this year’s election is rigged — although this time Mr. Trump’s campaign appears to be largely acting behind the scenes.
The theories are rampant on social media and widely embraced by activists. They have frequently shown up in the blitz of lawsuits that Republicans have filed in the run-up to the election, including a Georgia lawsuit that a judge dismissed this month, calling the security concerns about voting machines raised in the suit “purely hypothetical.”
Mr. Trump’s name was not on the suit, nor was the Republican National Committee’s. But text messages reviewed by The New York Times suggest that the former president’s top aides were behind it.
The lawsuit was filed by a county Republican Party only after the state Republican Party in Georgia refused, despite requests from “Trump inner circle/high up in RNC,” Alex B. Kaufman, the state party’s general counsel, wrote in a text to another Republican official last month.
“We had immense pressure from above and below to bring this, and said absolutely not,” he added in another message.
Josh McKoon, the chairman of the Georgia Republican Party, denied that the Republican National Committee or the Trump team had asked the state party to file the lawsuit.
“I, at no time, was under any pressure from anyone,” he said.
The Trump campaign and Mr. Kaufman did not immediately respond to requests for comment.
Theories about voting machines were some of the most far-fetched and easily debunked of the claims that Mr. Trump tossed out in his attempt to hold on to power after his defeat in 2020. Mr. Kaufman, in his texts, said the state party’s priority was “protecting sensible” election rules. While the machines are not without potential vulnerabilities, there has been no evidence to support the conspiracy theories that have proliferated — the most prominent being that the machines are programmed to flip votes away from Mr. Trump…