The Florida governor, Ron DeSantis, predicted a “cold war” with Georgia if it elects the Democrat and voting rights campaigner Stacey Abrams as governor this year.

“If Stacey Abrams is elected governor of Georgia, I just want to be honest, that will be a cold war between Florida and Georgia,” DeSantis said at a press event in the north-west of his own state.

“I can’t have [former Cuban leader Raúl] Castro to my south and Abrams to my north, that would be a disaster. So I hope you guys take care of that and we’ll end up in good shape.”

DeSantis polls strongly among potential Republican nominees for president in 2024, with or without Donald Trump in the race. Accordingly, he has positioned himself as a major player on culture-war issues, recently signing a bill regarding the teaching of LGBTQ+ issues which critics labeled “don’t say gay”.

In California, Los Angeles county has banned business travel to Florida and Texas over anti-LGBTQ+ policies. Such moves have also led DeSantis into direct confrontation with Disney, a major employer and economic engine in his state.

On Friday, he said: “I don’t really care what the media says about that. I don’t care what, you know, very leftwing activists say about that. I do not care what big companies say about that. We are standing strong. We will not back down on that.”

Abrams has become a major player in her own state and a hate figure among conservatives. A former state representative and a successful author, she ran for governor in 2018 and lost narrowly to Brian Kemp, refusing to concede while protesting his role as secretary of state in controlling his own election.

Abrams’ work to turn out Democratic votes, particularly among minorities, helped flip Georgia to Joe Biden in the 2020 presidential election and then elect two Democratic senators in runoffs in January the following year.

She is running unopposed in the Democratic gubernatorial primary this year but trails both the incumbent governor, Kemp, and his Trump-backed primary challenger, former senator David Perdue, in early polling.

Abrams did not immediately comment on DeSantis’s comment.

A spokeswoman for DeSantis’s office said: “If Stacey Abrams wins the governorship of Georgia, we know that her approach to leadership will involve more heavy-handed government, taxes and bureaucratic influence.”

Amid controversy, Craig Pittman, a Florida reporter and author, said the governor was “trying desperately to get attention from Fox News for saying something outrageous to own the libs and diss Black people”.