Former Senator David Perdue of Georgia, a Republican who is running for governor with the backing of former President Donald J. Trump, filed a lawsuit on Friday seeking the inspection of absentee ballots in the 2020 election, reviving long-debunked claims in the latest sign that Mr. Trump’s election grievances will be central to his candidacy.

The lawsuit draws on Mr. Trump’s false claims of election fraud in Georgia and across the country, which culminated in the Capitol riot on Jan. 6. In the months since, many Republican elected officials have pivoted from rebuking election conspiracy theories to embracing them vocally in an effort to win the affections of Mr. Trump and his supporters.

Mr. Perdue, who was endorsed by Mr. Trump soon after announcing his candidacy on Monday, is running against Gov. Brian Kemp, a fellow Republican who is a staunch conservative but has come under withering attacks from the former president and his allies over Mr. Kemp’s unwillingness to help them overturn President Biden’s victory in Georgia. Mr. Perdue told news outlets this week that he would not have certified the results if he had been governor instead of Mr. Kemp.

Republicans in states across the country have continued to cast doubt on the 2020 election’s legitimacy by trying to carry out partisan reviews of the results, which they often misleadingly label “audits” to lend them a greater sense of authority. G.O.P. lawmakers in at least five states are pursuing reviews, and Republicans in states including Oklahoma, Tennessee and Florida have introduced bills to begin new ones next year.

Mr. Perdue’s suit, which The Atlanta Journal-Constitution earlier reported and which was filed in the Superior Court of Fulton County, argues that through unlawful “acts and omissions,” election officials in Fulton, the state’s most populous county and a major source of Democratic votes, “circumvented the majority vote of the people of the State of Georgia and thereby affected the outcome of the statewide General Election on Nov. 3, 2020 in several races.”

In the complaint, Mr. Perdue names a county election official and workers underneath him, claiming that they “negligently, grossly negligently or intentionally engaged in and/or permitted multiple unlawful election acts.”

“David Perdue wants to use his position and legal standing to shine light on what he knows were serious violations of Georgia law in the Fulton absentee ballot tabulation,” Bob Cheeley, a lawyer for the candidate, told The Journal-Constitution.

Georgia election officials have reviewed the 2020 results three times and have come to the same conclusion: Mr. Biden won the state, narrowly but decisively.

Mr. Perdue lost his re-election bid in January to Senator Jon Ossoff, a Democrat.

The legal effort by Mr. Perdue follows a similar lawsuit this year by a group of voters led by a known conspiracy theorist. That case, which sought to inspect all 147,000 absentee ballots in Fulton County, was thrown out after Judge Brian Amero of Henry County Superior Court ruled that the plaintiffs lacked standing and could not show any specific injury or harm.

Mr. Perdue’s lawsuit could work around at least part of Judge Amero’s ruling, because he was a candidate in the 2020 elections.

Several Republicans in Georgia criticized the suit.

“David Perdue is so concerned about election fraud that he waited a year to file a lawsuit that conveniently coincided with his disastrous campaign launch,” Cody Hall, a spokesman for Governor Kemp’s campaign, said. “Keep in mind that lawsuit after lawsuit regarding the 2020 election was dismissed in part because Perdue declined to be listed as a plaintiff.”

Brad Raffensperger, the Georgia secretary of state — who, like Mr. Kemp, has come under attack from fellow Republicans for resisting Mr. Trump’s election pressure — said in a statement: “Fake Trumpers like Perdue are trying to curry favor with the Trump base by pushing election conspiracy theories that everyone — including the voters they are hoping to attract — knows they don’t really believe.”

Georgia continues to be a hub of litigation and national attention over elections and voting rights. Two election workers in the state filed a defamation lawsuit last week against Gateway Pundit, a right-wing news outlet that falsely claimed they had manipulated ballots. On Friday, Reuters reported that one of the workers said she had been pressured by a publicist for Kanye West, the rapper who ran for president and previously supported Mr. Trump, to acknowledge manipulating votes.

The Georgia Democratic Party, whose likely nominee for governor, Stacey Abrams, announced her campaign last week, reveled in the high-profile clash of Republicans and sought to lump them together.

“It is reprehensible that David Perdue is peddling those same dangerous lies in a sad ploy for attention,” the party said in a statement. “From David Perdue’s frivolous lawsuit to Brian Kemp’s voter suppression laws — both based on the same fabricated lies — nobody who sows distrust in our free and fair elections deserves to lead our state.”

Sheelagh McNeill contributed research.