• Georgia's Republican Gov. Brian Kemp was projected to win his party's nomination for reelection.
• Kemp is projected to defeat ex-President Donald Trump's preferred candidate, former Sen. David Perdue.
• Kemp will face Democrat Stacey Abrams in a rematch of the gubernatorial contest she narrowly lost to him in 2018, NBC News projected.

Georgia's Republican Gov. Brian Kemp was projected on Tuesday to win his party's nomination for reelection, batting away a primary challenge from ex-President Donald Trump's preferred candidate, former Sen. David Perdue.

Kemp will face Democrat Stacey Abrams in a rematch of the gubernatorial contest she narrowly lost to him in 2018, NBC News projected.

In a victory speech Tuesday night, Kemp vowed to beat Abrams again. He also accused her of viewing the governor's office as a "stepping stone" toward a presidential run, and slammed her for remarking over the weekend that Georgia's low national rankings in mental health, maternal mortality and other issues make it "the worst state in the country to live."

Abrams' campaign swung back at Kemp in a statement Wednesday, calling him "a failed governor who has disqualified himself from a second term" through his backing of a restrictive abortion law and a bill to loosen concealed-carry rules.

"Years from now, Kemp will be remembered as a one-term governor who pointed a gun at a boy on television," said the statement from Abrams campaign manager Lauren Groh-Wargo. She was referring to one of Kemp's 2018 campaign ads, which portrays Kemp holding a shotgun in his lap as he talks to a boy asking for permission to date one of his daughters.

Early polls of a Kemp-Abrams matchup show the incumbent governor with an average lead of about 5 percentage points, according to RealClearPolitics.

Kemp earned Trump's ire by certifying President Joe Biden's win over Trump in Georgia in the 2020 election, making Biden the first Democratic presidential candidate in decades to win the state. Trump has falsely claimed that that race and others were rigged against him through widespread voter fraud. He pushed Kemp to take steps to overturn Georgia's election results, but the governor refused.

Trump also endorsed Rep. Jody Hice, R-Ga, who mounted a primary challenge against Republican Secretary of State Brad Raffensperger, another of Trump's perceived enemies. Raffensperger rebuffed Trump's request to "find" enough votes in Georgia for him to win in 2020.

Both Perdue and Hice have echoed Trump's election claims. Reviews of ballots conducted by state and federal officials found no evidence of widespread voter fraud; William Barr, Trump's attorney general at the time, came to the same conclusion. Dozens of lawsuits filed by Trump and his allies failed to change any state's election results.

The primary races in Georgia, a swing state that narrowly voted for Biden in the 2020 presidential election, also mark the biggest test to date of Trump's enduring influence over the Republican Party.

Trump has touted the fact that most of the candidates he endorsed in the 2022 election cycle have won their primaries, though many of those races were not competitive. Fifteen months after his single term in the White House, the former president has held his status as the de facto leader of the GOP. Many Republican primary candidates have tried to appeal to the party's base by talking up their pro-Trump credentials, even if the former president did not endorse them.

The primary elections will set the table for the November midterms, when Republicans hope to win majority control of the House and Senate. Democrats are fighting uphill: The president's party tends to underperform in the midterm elections, and the lead-up to the primaries has been marked in part by high inflation and low approval ratings for Biden.