Former President Donald J. Trump suggested without evidence on Saturday that Georgia’s Republican governor was hampering his efforts to win the battleground state in November, a claim that carried echoes of Mr. Trump’s attempt to overturn his defeat to President Biden there in 2020.

“In my opinion, they want us to lose,” Mr. Trump said, accusing the state’s governor, Brian Kemp, and its secretary of state, Brad Raffensperger, who is also a Republican, of being disloyal and trying to make life difficult for him.

At a rally at the Georgia State University Convocation Center in Atlanta, in a speech that lasted more than 90 minutes and that was peppered with grievances about his loss four years ago, Mr. Trump falsely claimed, “I won this state twice,” referring to the 2016 and 2020 elections.

Mr. Trump lost to Mr. Biden by roughly 12,000 votes in Georgia in 2020. Last year, the former president was indicted by an Atlanta grand jury on charges related to his efforts to subvert the results of that election in that state. On Saturday, he complained that he might have avoided legal jeopardy if Mr. Kemp and Mr. Raffensperger had cooperated with his attempts to reverse the 2020 results.

Mr. Trump added that he thought Georgia had slipped under Mr. Kemp’s leadership. “The state has gone to hell,” he said.

Mr. Kemp, who indicated in June that he had not voted for Mr. Trump in the Republican primary this year, said on X that his focus is “on winning this November” and “not engaging in petty personal insults, attacking fellow Republicans, or dwelling on the past.”

“You should do the same, Mr. President, and leave my family out of it,” he said, sharing a social media message that Mr. Trump had posted earlier Saturday in which he jabbed at Mr. Kemp and Mr. Kemp’s wife.

Mr. Raffensperger shared a screenshot of the same post from Mr. Trump and said: “History has taught us this type of message doesn’t sell well here in Georgia, sir.”

Mr. Trump held his rally in Atlanta in the same arena where his Democratic opponent, Vice President Kamala Harris, held a rally earlier in the week. Both candidates filled the complex, which holds 8,000 people, though Mr. Trump, who has long bragged about his ability to draw overflow crowds, questioned whether Ms. Harris’s supporters had in fact come to hear the hip-hop star Megan Thee Stallion, who performed at that event.

Mr. Trump recalled that Bruce Springsteen had performed at a rally for Hillary Clinton in 2016. “I’m not a huge fan,” he said of Mr. Springsteen. “I have a bad trait. I only like people that like me.”

Mr. Trump, who was preceded onstage by his running mate, Senator JD Vance, repeatedly leveled personal attacks against Ms. Harris. He mocked the pronunciation of her first name, insulted her intelligence and communication skills, and called her a “radical left freak.”

“Kamala,” Mr. Trump said, enunciating with derision the syllables of her name. “You know there’s about 19 different ways of saying it. She only likes three.”

The Harris campaign provided a statement on Saturday night from Geoff Duncan, a Republican who was the lieutenant governor of Georgia during the 2020 election, denouncing Mr. Trump.

“Tonight, we heard a particularly unhinged, angry version of the same Donald Trump that Georgia rejected in 2020,” said Mr. Duncan, who has endorsed Ms. Harris.

Mr. Trump, who has been criticized for his past praise of dictators and authoritarian leaders, also suggested that Russia had managed to get the better end of a major prisoner swap with the Biden administration this week, which resulted in the release of the Wall Street Journal reporter Evan Gershkovich and the security contractor Paul Whelan.

“I’d like to congratulate Vladimir Putin for having made yet another great deal,” Mr. Trump said of the Russian president.

He added: “Boy, we make some horrible, horrible deals.”