President Trump picked a new fight Saturday with Georgia’s Republican governor as he campaigned in the key swing state where he’s looking to avenge his narrow 2020 loss — a defeat he continues to blame on GOP officials for not giving into his false theories of election fraud.

Trump attacked Governor Kemp on his social media site before his rally and said Mr. Kemp should be “fighting Crime, not fighting Unity and the Republican Party.” He also criticized Mr. Kemp’s wife, Marty, for saying she would write in her husband’s name for president this fall instead of voting for the Republican nominee.

At Saturday’s rally, Trump assailed Mr. Kemp in a roughly 10-minute tirade, blaming him for his loss to President Biden and for not stopping a local district attorney from prosecuting him and several associates for his efforts to overturn the results.

“He’s a bad guy. He’s a disloyal guy. And he’s a very average governor,” Trump said. “Little Brian, little Brian Kemp. Bad guy.”

On X, Mr. Kemp told Trump to “leave my family out of it” and urged him to stop “engaging in petty personal insults, attacking fellow Republicans, or dwelling on the past.”

Georgia is likely to see another closely contested election as both campaigns push hard in the state, with Democrats riding a new wave of enthusiasm after Mr. Biden dropped his reelection bid and endorsed Vice President Harris. To win this time, Trump will likely need the support both of Kemp’s political operation and from moderate and conservative voters who aren’t as committed to him as members of his base.

Going to Atlanta put Trump in the state’s largest media market, including suburbs and exurbs that were traditional Republican strongholds but have become more competitive as they’ve diversified and grown in population. Thousands of supporters packed the same arena for a Harris rally days earlier.

A 23-year-old who works in the trucking industry and drove from Heflin, Alabama, just across the western Georgia border to attend his third Trump rally, Draic Coakley, said he believes Trump “sees people like me,” while “Biden and Harris, well, are part of what I think of as the elite.”

“President Trump may be a billionaire, but it’s OK to be rich,” Mr. Coakley said. “He gets us. He just gets us, and he gets the country.”

Mr. Biden beat Trump in the state by 11,779 votes in 2020. Trump pressured Georgia’s Republican secretary of state, Brad Raffensperger, to “find” enough votes to change the outcome and his allies tried to present slates of so-called “fake electors” that could replace the Democratic voters Mr. Biden won.

Trump was later indicted in Georgia for his efforts to overturn the election, but the case remains on hold while courts decide whether the Fulton County district attorney can continue to prosecute it.

Mr. Kemp certified the electors that Mr. Biden won four years ago and repeatedly rejected efforts by Trump allies to replace them. He’s since proven to be the rare Republican nationally who could hold his ground against Trump without sacrificing his power or popularity, with 63 percent of Georgians approving of his job performance in a June poll conducted for the Atlanta Journal-Constitution.

Mr. Kemp won the governor’s office narrowly in 2018 after garnering Trump’s endorsement. But Trump backed a primary rival against Mr. Kemp in 2022 — David Perdue, who spoke at Saturday’s rally. Mr. Kemp trounced Mr. Perdue on his way to defeating Democrat Stacey Abrams, a national star in her party, by 7.5 percentage points, a veritable blowout in a battleground state.

Mr. Kemp will chair the Republican Governors Association for the 2026 election cycle, when he is leaving office. And he’s widely known to be national Republicans’ top choice to take on Senator Ossoff in that midterm cycle.

Kemp has said he didn’t vote for anyone in this year’s primary but will vote for the Republican ticket in November.

A prominent conservative host in Georgia, Erick Erickson, said of Trump, “He can’t help himself.”

“Donald Trump is really trying to build unity in Georgia by attacking the sitting Republican Governor whose ground game he will need to win and also that Governor’s wife,” Erickson wrote on X. “And if he loses, it’ll be because of this stuff, not a stolen election.”