(CNN) Democratic nominee for Florida governor Andrew Gillum isn't worried about the possible influence President Donald Trump will have on his race against Republican Ron DeSantis in the general election this November.

"I actually believe that Florida and its rich diversity are going to be looking for a governor who's going to bring us together, not divide us. Not misogynist, not racist, not bigots," Gillum told CNN's John Berman on "New Day" Wednesday morning, following his primary victory Tuesday night.

He added, "They're going to be looking for a governor who is going to appeal to our higher aspirations as a state. Who's going to talk about what it means to build a Florida that makes room for all of us and not just some of us."

Gillum made history Tuesday night as the first black candidate to win a major-party gubernatorial nomination in Florida. His surprise upset win Tuesday night was also a major victory for the Democratic Party's progressive wing.

The race pits Gillum, a Bernie Sanders-backed progressive candidate, against DeSantis, who has Trump's endorsement, in what is a major test of the political atmosphere. On Tuesday, after clinching the GOP nomination, DeSantis credited the President for helping boost his candidacy.

Read More