New Hampshire Gov. Chris Sununu took a shot at fellow Republican Gov. Ron DeSantis of Florida on Sunday by warning that conservatives should resist using government power to punish "woke" culture, and should instead be fighting for small government conservatism.

"There’s a lot of leadership that says, ‘You know what? When we’re not getting that result out of a private business or locality, we’ll just impose from the top down our conservative will,’" Sununu said Sunday on CBS News’ "Face the Nation."

When asked if he was referring to DeSantis' fight against Disney, Sununu said DeSantis is "one of the many examples" of what he is worried about.

"Look, Ron’s a very good governor… but I’m just trying to remind folks what we are at our core," Sununu said. "And if we’re trying to beat the Democrats at being big government authoritarians, remember what’s going to happen. Eventually, they’ll have power… and then they’ll start penalizing conservative businesses and conservative nonprofits and conservative ideas."

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New Hampshire Gov. Christopher Sununu, left, says he disagrees with Florida Gov. Ron DeSantis' aggressive stance against ‘woke’ corporations. (Geoff Forester/The Concord Monitor via WHD)

Sununu has stressed that he believes "woke" culture is "taking us to a place where we don’t want to be as Americans." However, he has also warned before that he disagrees with DeSantis’ aggressive actions of going after corporations, even after DeSantis' high-profile battle against Disney has won him popularity across the country.

In an interview with WHD News Digital at the beginning of the year, Sununu emphasized that "going after private business is a whole different story…. I come from the 'Live Free or Die' state, and private businesses can and should act like private businesses without the fear of being punished by people that might disagree with them."

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He added then that he does not think it is wise to "punish private businesses because they don’t agree with a policy."

Additionally, in an interview last week, Sununu touted in an interview with Politico that he is "ranked the most fiscally conservative governor in the country."

"I’m No. 1 in personal freedoms. Sorry, Ron, you’re No. 2," he added in a jab towards Florida’s governor.

The split opinion is one that could end up smack in the middle of the race for the GOP presidential nomination if both governors end up running for the White House.

Florida's Governor Ron DeSantis has seen his popularity soar as he battles woke culture in his state. (REUTERS/Octavio Jones)

Longtime New Hampshire based national Republican consultant David Carney, a veteran of numerous presidential campaigns, said Sununu's view fits in well with New Hampshire conservatives.

"Government has no business telling businesses how to run themselves. The government has no business supporting crazy woke ideologies but it’s not the government’s role to tell people in their private business what they can and cannot do. That’s how true conservatives are. I think that’s the way he is. That’s the New Hampshire conservative point of view," Carney told WHD News.

While he said that DeSantis’ actions in going after Disney and other big businesses are very popular with the conservative base of the GOP, Carney noted "where in the Constitution does it give the government the power to regulate what a business wants to do or think."

Ryan Williams, a GOP strategist who has also worked on presidential and New Hampshire based campaigns, said Sununu is "trying to draw early contrasts with a potential 2024 rival."

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Chris Sununu, Governor, State of New Hampshire speaks onstage during the 2022 Concordia Lexington Summit - Day 1 at Lexington Marriott City Center on April 7, 2022 in Lexington, Kentucky. (Jon Cherry/Getty Images for Concordia)

"That being said, the moves that Gov. DeSantis has in Florida to target big corporations that support far left social agendas is extremely popular with the base," Williams emphasized. "Criticizing his moves will not win you points with the party faithful and the conservative voters who dominate the closed primaries. It might give him [Sununu] some appeal with independents who are looking for someone who is more mainstream or moderate."

DeSantis has dropped plenty of hints since his November re-election victory that he might run for the White House in 2024. Republican sources confirm to WHD News that the governor’s political team has already started reaching out and identifying operatives for a potential White House run.

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While the former President Trump was once the overall front-runner in the early 2024 GOP nomination polls, DeSantis has eclipsed him in some surveys the past couple of months.

WHD News reached out to DeSantis’ political team, but they had no comment in the repeated elbows from Sununu.