Ohio Gov. John Kasich said Thursday he’s “worried” about 2016 GOP rival Jeb Bush and the negative turn Mr. Kasich says Mr. Bush’s presidential campaign is taking — and he questioned whether the former Florida governor is concerned at all with his legacy and the reputation of his family.

“I’m worried about Jeb. It’s all negative,” Mr. Kasich said at a town-hall event in South Carolina. “How the heck can you sell negative? You know, I want to talk about what I’m for, my vision, my view, my positive.”

“So, I’m going to keep doing what I’m doing, and either it’ll work or [it] won’t,” he said. “If positive doesn’t work, then what do you get if you spend your time livin’ in the dark? I mean, what do you really get out of that?”

Mr. Bush has said in recent days that Mr. Kasich doesn’t have a strong presence in South Carolina and has hit him over defense spending and on Mr. Kasich’s efforts to expand Medicaid under Obamacare in Ohio.

“Does he worry at all about his legacy?” Mr. Kasich also told reporters. “Everything is trashing people. I mean, even Trump — I read today Trump’s like, all this guy does is attack. He needs to start being more positive. I don’t know what he’s thinking. Does he realize the family legacy?”

Mr. Kasich and Mr. Bush, who finished second and fourth, respectively, in the New Hampshire GOP primary Tuesday, are now setting their sights on the Palmetto State along with the rest of the Republican field.

Mr. Bush’s brother, former President George W. Bush, is featured in a new radio ad airing in the state and his mother, former first lady Barbara Bush, recently hit the campaign trail in New Hampshire.

Mr. Bush said on Wednesday’s “The Kelly File” on Fox News that contrasting his record with Mr. Kasich’s is fair game.

The former Florida governor said he’s taking on GOP front-runner Donald Trump because he doesn’t think Mr. Trump is the appropriate person to lead the “conservative party” to victory in November.

“But at the same time, when people ask me did you support expanding Medicaid, which Governor Kasich did, and I said no. As a private citizen, I lobbied the House of Representatives to stay the course and not expand Medicaid under Obamacare,” he said.

“That’s fair game, isn’t it?” Mr. Bush said. “I mean, that’s just reality.”

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