The former president is leading all other Republican candidates for the party’s presidential nomination, with Mr DeSantis running in second place, according to polls.
The Florida governor officially launched his own bid earlier this week in a chaotic Twitter Spaces event with billionaire Elon Musk.
And Mr DeSantis told radio host Matt Murphy that he was running to the right of Mr Trump and portrayed himself as more conservative, according to USA Today.
“It seems like he’s running to the left and I have always been somebody that’s just been moored in conservative principles,” said Mr DeSantis.
“So these will be interesting debates to have, but I can tell you, you don’t win nationally by moving to the left, you win nationally by standing for bold policy. We showed that in Florida. I never watered down anything I did.”
And Mr DeSantis claimed that Mr Trump is not the same person who first ran for office.
“I don’t know what happened to Donald Trump; this is a different guy today than when he was running in 2015 and 2016 and I think the direction that he’s going with his campaign is the wrong direction,” Mr DeSantis said.
And he attacked Mr Trump over his handling of the Covid-19 pandemic while in office.
“I think [Trump] did great for three years, but when he turned the country over to Fauci in March of 2020 that destroyed millions of people’s lives,” Mr DeSantis said on a podcast.
“And in Florida, we were one of the few that stood up, cut against the grain, took incoming fire from media, bureaucracy, the left, even a lot of Republicans, had school open, preserved businesses.”
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