GRIFFIN, Ga. — Sen. David Perdue was encouraging a crowd at a gun club south of Atlanta to support him and fellow Republican Kelly Loeffler in their bid for Georgia’s Senate seats, which he called the only thing standing between America and “a radical socialist agenda.”

But five minutes into the senator’s speech, a man interrupted.

“What are you doing to help Donald Trump and this fraud case?” the man screamed, as one woman said “Amen” and the crowd applauded. “What are you doing to stop what’s been going on here and this election fraud?”

The Republican candidates in Georgia’s dual Senate runoff campaign are navigating a highly unusual political labyrinth – caught in the middle of an intraparty war that has erupted since President Trump narrowly lost the state to President-elect Joe Biden and has turned his fire on the Republican leadership there.

The infighting now threatens to turn off the very Republican voters Perdue and Loeffler need to stave off challenges from their Democratic rivals, Jon Ossoff and the Rev. Raphael Warnock.

Trump and his allies have repeatedly, and falsely, accused Georgia Secretary of State Brad Raffensperger and Gov. Brian Kemp, both Republicans, of presiding over a fraudulent election.

Trump has pushed the baseless claim that the Dominion Voting Systems machines used in Georgia were rigged as part of a global conspiracy, and Perdue and Loeffler have called for Raffensperger’s resignation.

But therein lies the conundrum: Perdue and Loeffler are traveling the state pleading with Republican voters to turn out on Jan. 5 – effectively asking Trump supporters to put their faith in the same voting system their president claims was manipulated to engineer his defeat.

Loeffler and Perdue are walking what one Republican strategist called “a high-wire act right now, to figure out exactly where the candidates should be relative to the president.”

Complicating the senators’ pitch to voters is the call by some Trump advocates for voters to protest the voting system in ways that some Republican strategists fear will merely result in effective votes for the Democrats.

One prominent Trump ally, Atlanta attorney Lin Wood, who unsuccessfully sued Georgia election officials to stop the certification of the vote, has urged Republican voters not to vote in elections with Dominion machines.

Wood has attacked Perdue and Loeffler for not doing enough to help, and told his 631,000 Twitter followers last weekend that if the senators don’t step up their support, he would take a pass on Jan. 5.

“If not fixed, I will NOT vote in GA runoff,” he tweeted.

Asked whether his efforts would depress GOP turnout, Wood told The Washington Post via email that the Dominion machines “have no integrity” and insisted that “Georgia can vote by written ballot if necessary in January.”

Raffensperger, among the most outspoken who have said such talk will hurt Loeffler’s and Perdue’s chances, expressed exasperation at Wood’s comments. A statewide audit of the presidential result, in which every ballot was recounted by hand, disproved the claims about the voting machines.

“I really don’t know what he’s thinking,” Raffensperger said in an interview.

“If the people don’t use the machines, then I guess they vote absentee and then their ballot will be scanned on a Dominion machine,” he said.

“People need to get a grip on reality.”

And the state Republican chairman, David Shafer, has echoed questions about the state’s voting system. He signed a letter along with the state party executive committee demanding fresh scrutiny of signature verification on mail-in ballots.

No evidence has surfaced that ballots with nonmatching signatures were counted.

Trump has tweeted in favor of Loeffler and Perdue, but he has not committed to showing up on the campaign trail, though Vice President Mike Pence did lead a rally.

Kemp, the governor, has also avoided making any runoff campaign appearances on behalf of his state’s two Republican senators. The governor has been walking a line between supporting the integrity of the election result – he signed the certification on Friday of the presidential race votes – and agreeing that improvements can be made to signature verification and voter-identification rules.