Trump played down suggestions of a feud with DeSantis, calling him a “fine guy” as he spoke to the media on his 757 jet, nicknamed “Trump Force One”.
“There’s not a tiff with me,” he said. “I’m way up in the polls, which people hate to say. I don’t think I’d have any trouble defeating him.”
But he urged DeSantis not to run, saying: “I think he would be making a mistake, I think the base would not like it. I don’t think it would be good for the party.”
Trump added: “I don’t know that he’s running. I think if he runs he could hurt himself very badly, I really believe he could hurt himself badly”.
The former president also said he did not think Joe Biden would run again in 2024. He said: “I don’t think he runs. It is inconceivable”.
Trump confirmed that, as a Florida resident, he had voted for his rival DeSantis to be re-elected as the state’s governor.
As he left a polling station in Florida, Trump was asked if he had voted for Governor DeSantis. He said: “Yes I did.”
Trump used an election eve rally in Ohio to declare he would make a statement on Tuesday, November 15 at his Mar-a-Lago resort in Florida.
It was read as confirmation that he will make a third run for the White House.
The choice of November 15 is three days after Trump’s youngest daughter, Tiffany, is due to be married at Mar-a-Lago.
The date also coincides with the publication of an insider’s account of the Trump administration by Mike Pence, Trump’s former vice president, and is likely to overshadow its release.
Marc Short, a former aide to the vice president, said Trump’s decision to make an announcement on the same day “wouldn’t be out of character”.
Trump would enter the 2024 race with more than $60 million in cash held by his Save America political organisation, but once he formally declares a number of election laws will dictate spending of the war chest.
During his 90-minute speech in Ohio, Trump said he was confident Republicans would take back Congress and return to the White House in 2024, criticising Joe Biden’s performance.
But much of his time in the spotlight on election eve was dedicated to his familiar complaints about the media, House Speaker Nancy Pelosi, and the Democrats who twice voted to impeach him from office.
Earlier in the speech, Trump called Ms Pelosi an “animal”. The senior Democrat’s husband was violently assaulted by an intruder in their home who had been searching for her last month.
“She impeached me twice for nothing. Nothing,” Trump said.
Earlier, Trump set off a last-minute scramble among the Republican Party’s top officials by threatening to announce his bid at the rally in Ohio and upend yesterday’s midterm elections.
It prompted a frenzied chain of phone calls from rattled senior Republicans, who for months have attempted to stop Trump from overshadowing the elections that will determine control of Congress.
The party’s leaders feared an election-eve declaration would spur higher turnout among Democrats and potentially tip the balance in razor-thin races for the Senate.
Trump was ultimately persuaded that his announcement would be drowned out by the tide of election news.
He told supporters in Ohio, who had gathered for the state’s Republican senate candidate JD Vance: “We want nothing to detract from the importance of [the midterms]”.