John R. Bolton, who fervently disavowed former President Donald J. Trump after serving as his national security adviser, said on Wednesday that he would be voting for a Republican in the November election, just as he did four years ago — only not for his old boss but for former Vice President Dick Cheney.

Mr. Bolton, a fixture in multiple Republican administrations and a former diplomat, revealed his choice for president in an appearance on CNN. It was the same person, he said, whom he wrote in during the 2020 election.

“I might as well say it now: I voted for Dick Cheney,” he said. “And I’ll vote for Dick Cheney again this November.”

Mr. Bolton worked alongside Mr. Cheney, whom he described as a “principled Reaganite conservative,” in the administration of President George W. Bush, including as ambassador to the United Nations. Mr. Cheney is 83, nearly two years older than President Biden (who is 81) and about five-and-a-half years older than Mr. Trump (who is 77).

“Age is no longer a factor in American presidential politics, so his age doesn’t disqualify him,” Mr. Bolton said of Mr. Cheney. “And I think he’d do an immensely better job than either Trump or Biden.”

In 2020, Mr. Bolton published a scathing tell-all memoir about his dealings with Mr. Trump, whom he portrayed as corrupt, poorly informed and reckless. An updated edition of Mr. Bolton’s book released this year warned that a second Trump presidency would focus on retribution.

Mr. Trump has repeatedly assailed his onetime national security adviser, calling him a “wacko” and a “boring fool who only wanted to go to war” in a social media post in 2020.

“Never had a clue, was ostracized & happily dumped,” Mr. Trump wrote of Mr. Bolton’s departure from his administration.

On Wednesday, Kaitlan Collins of CNN asked Mr. Bolton whether he would consider supporting Liz Cheney, Mr. Cheney’s eldest daughter and a former House member from Wyoming whose criticism of Mr. Trump prompted her defeat in the Republican primary in 2022.

“Well, I like Liz a lot,” he said. “And maybe someday she’ll get my write-in vote, too, but right now I’ll stick with her father.”

Mr. Cheney could not be immediately reached for comment on Thursday.

Mr. Bolton belongs to a cohort of former Trump administration officials who have said they will not vote for the former president or have declined to endorse him.

Mark Esper, whom Mr. Trump fired as defense secretary in the waning days of his presidency and who opposed his plan to deploy troops to quell protests in U.S. cities in 2020, told Bill Maher on “Real Time” in March that he would not support Mr. Trump this fall.

“There’s no way I’ll vote for Trump, but every day that Trump does something crazy, the door to voting for Biden opens a little bit more,” Mr. Esper said.

And Mike Pence, who was Mr. Trump’s vice president, told Fox News last month that he “could not in good conscience” endorse him. He declined to say whether he would vote for Mr. Trump in November, but added, “I would never vote for Joe Biden.”