ATLANTA — David Perdue, the former U.S. senator from Georgia and ally of Donald Trump, plans to announce Monday that he will run in a Republican primary against the state’s incumbent governor, Brian Kemp, according to sources familiar with Mr. Perdue’s plan. Mr. Trump has vowed to orchestrate Mr. Kemp’s defeat as payback for the governor’s refusal to help overturn the former president’s November election loss in the state.

The news of Mr. Perdue’s pending announcement, first reported Sunday in Politico, illustrates both the grip the former president still wields over the G.O.P. and his willingness to upend state races entirely because of his personal pique toward Republicans he feels are insufficiently loyal to him.

Mr. Perdue’s decision to try to knock out a fellow Georgia Republican in 2022 is also sure to ignite an ugly — and costly — intraparty war before a general election in which the Republican nominee will likely face Stacey Abrams, the Democratic superstar whose national fame will allow her to amass a huge campaign war chest. Ms. Abrams, who lost to Mr. Kemp in 2018, announced her own run for governor last week.

Ms. Abrams’ announcement accelerated Mr. Perdue’s decision, moving up his timeline to before the new year. The former senator has told people he was uncertain about running but decided to run because he’s gravely worried about her prospects for victory over an incumbent who has been weakened by Mr. Trump’s unrelenting attacks.

Mr. Perdue, 71, a wealthy former corporate executive, narrowly lost his U.S. Senate seat to Jon Ossoff, a Democrat, in a January runoff. Reports about his return, this time as a candidate for governor, have been circulating for weeks. A number of Republicans told The Atlanta Journal-Constitution in October that Mr. Perdue was considering the move. At a September rally in rural Georgia, Mr. Trump appeared to encourage Mr. Perdue to challenge Mr. Kemp, who is seeking a second term.

Mr. Trump, standing at a lectern, turned to Mr. Perdue and praised him as a “great guy.”

“Are you going to run for governor, David Perdue?” he asked.

Mr. Trump then went on to accuse Mr. Kemp, 57, a former Trump favorite, of being a “RINO governor,” meaning “Republican in name only.” He also described him as “a complete and total disaster on election integrity.”

The looming battle between Mr. Perdue and Mr. Kemp will help determine the extent of Mr. Trump’s influence heading into Georgia’s crucial 2022 general election. Mr. Trump has been working to set up a pro-Trump Republican slate in Georgia made up of politicians who have supported his false assertions that the 2020 presidential election was somehow “rigged.” The list so far includes the former football star Herschel Walker, who is running for U.S. Senate; U.S. Representative Jody Hice, who is running for secretary of state; and State Senator Burt Jones, who is running for lieutenant governor.

The outcome of the Georgia elections will have important implications for the country. Raphael Warnock, the other Democratic senator from Georgia who won a January runoff race, is up for election in 2022, and that contest may help determine which party controls the Senate. And with Ms. Abrams in the race, the election will serve as a dramatic plot point in the closely watched story of one of the Democratic Party’s most respected and ambitious politicians.

Ms. Abrams lost to Mr. Kemp in the 2018 governor’s race by about 55,000 votes. But the result was close enough to convince many observers that Georgia, once reliably Republican, had become a true battleground state. And Ms. Abrams’s organizing prowess is believed to have helped pave the path to victory for Senators Ossoff and Warnock, as well as President Biden, who also squeaked out an upset victory in Georgia.

In 2018, Mr. Kemp ran as a “politically incorrect conservative” candidate proudly in the Trump mold, armed with a pro-Second Amendment message, a hard-line illegal immigration stance and, crucially, the endorsement of Mr. Trump himself.

But the fact that Mr. Trump has unequivocally turned against Mr. Kemp — and is actively seeking vengeance — has created an awkward and potentially perilous situation for the governor. Polling commissioned by Mr. Trump’s Save America PAC released in August showed Mr. Kemp leading Mr. Perdue by six points among likely Republican primary voters. But the poll showed that if Mr. Perdue were endorsed by Mr. Trump, he would leapfrog ahead of Mr. Kemp.

Mr. Kemp, however, is a savvy politician and former two-term secretary of state well-known to Georgia Republicans. A campaign disclosure from July showed that he had amassed nearly $12 million. But some Republicans are concerned that he will have to spend dearly to fend off Mr. Perdue’s primary challenge. If he wins, he may find himself depleted financially as he heads into a general election against the formidable Ms. Abrams.

Some Republicans have quietly expressed surprise that Mr. Perdue would want to take on Mr. Kemp. Mr. Perdue did not seem to relish the down-and-dirty realities of running in a close race when Mr. Ossoff challenged him last year.

In February, Mr. Perdue said that he would not challenge Mr. Warnock in the Senate race. The New York Times reported at the time that Mr. Perdue, aware of Mr. Trump’s vengeful streak, was put off by the idea of running for office in 2022 — and of being involved in Mr. Trump’s plot to get even with the people on his enemies list, including Georgia’s Republican governor.