ATLANTA — Former Senator David Perdue’s leap Monday into a primary challenge against Gov. Brian Kemp, his fellow Republican, ensured that Georgia will be at the hot molten core of the political universe next year, with costly and competitive races that will test the grip of Trumpism over the G.O.P. and measure the backlash against President Biden in a state that increasingly reflects the country’s demography and its divisions.

Already a battleground at the presidential level, Georgia will be the scene of intense Republican primary showdowns for both governor and secretary of state, followed by general election contests in which Democrats — led by Senator Raphael Warnock, who is seeking a full term, and Stacey Abrams, who narrowly lost the 2018 governor’s race to Mr. Kemp and announced another bid last week — hope to keep the state a bluer tint of purple.

Mr. Perdue, who lost his Senate seat after one term to the Democrat Jon Ossoff in January, is former President Donald J. Trump’s preferred candidate, while Mr. Kemp earned a place on Mr. Trump’s enemies list after declining to help the former president overturn his 2020 election loss in Georgia. The two will now face off in May in an internecine war that may offer the closest approximation to a referendum on Trumpism next year as any in the country.

“Look, I like Brian. This isn’t personal,” Mr. Perdue said Monday in a video announcing his candidacy. But he implied that Mr. Kemp had damaged his standing with Georgia’s Trumpist base of Republican voters.

“He has failed all of us,” Mr. Perdue said of Mr. Kemp, “and cannot win in November.”

Aides to Mr. Kemp gave Mr. Perdue a blistering reception, revealing the depths of the anger over what they view as his betrayal of a fellow Republican and former political ally. They noted that the governor had actually beaten Ms. Abrams, while Mr. Perdue was, most recently, that most loathsome of nouns in the former president’s vocabulary: a loser.

And Georgians First Inc., a pro-Kemp political action committee, released an ad reminding voters of Mr. Perdue’s stock trades of companies whose business fell under the purview of his Senate committees.

While Mr. Kemp boasted a “proven track record,” a campaign spokesman for the governor, Cody Hall, said on Monday, “Perdue is best known for ducking debates, padding his stock portfolio during a pandemic, and losing winnable races.”

Endorsing Mr. Perdue on Monday, Mr. Trump called Mr. Kemp “a very weak governor” who “can’t win because the MAGA base — which is enormous — will never vote for him.”

In entering the governor’s race, Mr. Perdue joins a number of other G.O.P. candidates who could form a slate of high-profile Trump loyalists in November: The former football star Herschel Walker, with Mr. Trump’s encouragement, is seeking the nomination to run against Mr. Warnock. And Representative Jody Hice is challenging the Republican secretary of state, Brad Raffensperger, who also rebuffed Mr. Trump’s entreaties to help overturn his defeat.

Both Mr. Walker and Mr. Hice have parroted Mr. Trump’s false claim that election fraud cost him the 2020 election.

And Mr. Perdue did not limit his own attack to Mr. Kemp. Republicans were disunited in Georgia, he said, “and Brian Kemp and Brad Raffensperger are to blame.”

The influence of Mr. Trump, who has not ruled out another presidential run in 2024, is bound to be felt in other states’ midterm races. But Mr. Trump has been particularly fixated on Georgia, a state he lost by fewer than 12,000 votes. He and some of his allies are being investigated by the Fulton County district attorney’s office for potential criminal violations after reaching out to state officials, including Mr. Kemp and Mr. Raffensperger, in an effort to change the election results.

If Mr. Perdue and Mr. Walker lead the Republican ticket next fall, Georgia voters will be forced to choose between revulsion for Mr. Trump and his incendiary politics, on the one hand, and, on the other, dissatisfaction with Mr. Biden and unease with the liberal politics that Ms. Abrams and Mr. Warnock embody.

The drama will unfold in a state that, with its gaping divides along the lines of race, class and region, mirrors the nation and its partisan, polarized and increasingly poisonous politics.

Georgia also reflects broader trends among the two national parties. Democrats are increasingly turning to more diverse candidates. But the candidates are still stepping gingerly, as Ms. Abrams did in her launch video by trumpeting the idea of “one Georgia,” and seeking to elevate unifying issues that can appeal to die-hard liberals and fickle suburbanites alike.

Some Democrats fear that Ms. Abrams, a veteran state legislator and voting-rights advocate, may face an uphill climb in the governor’s race given the challenges confronting the party nationally: an unpopular president, inflation, Covid-19, and simmering concerns over violent crime and how American history is taught in schools.

But many expressed hope on Monday that the coming fight between Mr. Kemp and Mr. Perdue would benefit Ms. Abrams, who is seeking to become the state’s first Black governor, and other down-ballot Democrats.

“While David Perdue and Brian Kemp fight each other, Stacey Abrams will be fighting for the people of Georgia,” said her campaign manager, Lauren Groh-Wargo, pointing to Ms. Abrams’s stances on health coverage, school funding and Covid-related health policies.

For Republicans, Georgia has now become perhaps the most consequential proving ground in the party’s Trump wars. Should Mr. Perdue and other Trump-backed candidates lose their primaries, it will raise grave questions about the former president’s clout in the party as well as his own capacity to compete in a must-win state in 2024.

By running, Mr. Perdue and his supporters are effectively sending the message that Mr. Trump must be accommodated — and his election denialism perpetuated.

Mr. Perdue’s allies say their case is very simple: Mr. Kemp is unelectable next November because a significant number of Trump devotees will stay at home if he’s nominated.

“The bitterness between Kemp and Trump is so deep that Kemp cannot win a general election,” said Newt Gingrich, the former House speaker, who is backing Mr. Perdue. “The question for Georgia Republicans is would you like Perdue or Stacey Abrams, because if you’re for Kemp, you’re effectively voting for Stacey Abrams.”

For his part, Mr. Kemp, who in his 2018 race brandished guns and threatened to round up “criminal illegals” in his pickup truck, can be expected to remind Republican voters that it is hard to outflank him to the right on issues like gun control or abortion rights. He also signed into law Georgia’s controversial new voting law, which limits ballot access for voters in urban and suburban areas that are home to many Democrats.

Mr. Kemp’s supporters also say they believe that Ms. Abrams is enough of a polarizing force to cauterize any G.O.P. wounds sustained in the primary.

“She will inspire Republicans to come back out,” said Erick Erickson, a Georgia-based conservative writer and radio host. “They’re not going to stay home in Kemp-versus-Abrams or Perdue-versus-Abrams.”

Still, Mr. Erickson, an outspoken Trump detractor, expressed concern that a nasty primary could disrupt next year’s legislative session and deny Mr. Kemp any new accomplishments to run on.

Democrats, who are eager to amplify the opposition’s discord — and to downplay Mr. Biden’s unpopularity, which is weighing on the party in Georgia as elsewhere — can barely contain their glee.

“All that Perdue is going to be talking about is ‘the election was stolen,’” said Jennifer Jordan, an Atlanta-area state senator running for attorney general. “The voters in my district, the chamber of commerce Republicans, that is incredibly unseemly to them. You have this guy, Perdue, who had some appeal in the business community, and he’s basically giving that away because now he’s just going to become Trump’s boy.”

Andra Gillespie, an associate professor of political science at Emory University, said she expected Republicans to rally around the party’s nominee in November. But even if that were Mr. Kemp, she said, Mr. Trump could still be a wild card.

“If Brian Kemp won,” she said, “would Donald Trump be disciplined enough to keep his mouth shut in a general election?”