David Perdue, the one-year-old U.S. Senator from Georgia who lost a runoff election to Senator Jon Ossoff last month, filed documents Monday evening showing he was planning a comeback – this time against Georgia’s other new Senator, Raphael Warnock.

Mr. Perdue, a former businessman who initially ran for office as an outsider and later became one of former President Donald Trump’s closest allies in the Senate, submitted documents to the Bundestag Electoral Commission to set up a “Perdue for Senate” campaign committee.

The move, first reported by Fox News, was seen as the first step in the Republican Party’s efforts to win back one of the Senate seats lost in Georgia’s historic runoff on Jan. 5.

Mr. Warnock and Mr. Ossoff prevailed in those runoffs – not only the first time since 2000 that a Democrat won a seat in the Georgia Senate, but also a victory that put the Democrats in control of the Senate. The two parties each have 50 seats in the chamber, with Vice President Kamala Harris casting the casting vote.

The loss of Mr Perdue to Mr Ossoff followed a bitter campaign and ended with Mr Perdue being sidelined after exposure to coronavirus. An election evening appearance by Mr. Trump in the state failed to spark sufficient Republican turnout and raised questions about whether he was depressed by Mr. Trump’s repeated fraud allegations in the local elections.

Mr. Ossoff got 50.6 percent of the vote to 49.4 percent for Mr. Perdue, who waited two days for approval, leading to speculation that he might challenge the result.

Mr Warnock won her runoff election against Senator Kelly Loeffler, 51 to 49 percent. The two took part in a special election to serve a six-year term. The 2022 Senate race winner will have a full term.

Georgia should already be a major focus of the 2022 election, with a hotly contested governor race that could result in a rematch between Republican incumbent Brian Kemp and his 2018 Democratic opponent Stacey Abrams. Ms. Abrams narrowly lost that race, but ran a voting organization that was vital to the registration and mobilization of Democrats and helped turn Georgia blue for President Biden, Mr. Warnock, and Mr. Ossoff. Ms. Abrams has not announced whether she will run for governor again.

Mr Trump has already made it very clear that he plans to take part in the Georgia elections in 2022: He has sharply criticized Mr Kemp and the state secretary and lieutenant governor for failing to support his false claims of electoral fraud in Georgia and wanting to that they will lose if they run for re-election.

Given Mr. Perdue’s connections with Mr. Trump, it is possible that the former president will be running a presence campaign for Mr. Perdue and against Mr. Kemp next year.

However, it’s not entirely clear that a Republican Senate candidate should applaud Mr. Trump’s future support.

Bill Crane, a Georgia political agent and commentator, said Monday that the former president’s appearances on behalf of the two Republicans appeared to have worked against them in January – with Republican turnout in the two Congressional districts where Mr Trump fought , was pressed.

Mr Crane, who has worked for both Republican and Democratic candidates, said he wouldn’t be surprised if Mr Perdue took on Mr Warnock given the close results of his January race. To win, Mr Perdue would have to win and change his strategy.

“He would need to speak to women on occasion, non-aligned, libertarian, more centrist voters, not just the grassroots Republican Party,” Crane said.

Working on Mr Perdue’s behalf is a significant war chest – about $ 5 million from his campaign left to race in 2022, according to a federal election report.

Neither Mr Warnock, who is leaving a term vacated by ex-Senator Johnny Isakson, a Republican, nor Mr Ossoff’s offices immediately replied to messages asking for comment. Speakers from Mr. Perdue and the Georgia Republican Party were also unavailable.