John Kasich. Business Insider

Ohio Gov. John Kasich, who hosted a Fox News program from 2001 through 2007, said he "wouldn't have stayed" at the network if he had witnessed a culture of sexual harassment.

Kasich, speaking to Business Insider Monday while promoting his new book, "Two Paths: America Divided or United," responded to the recent ouster of the primetime host Bill O'Reilly.

O'Reilly was ousted after The New York Times reported the host and network had paid out more than $13 million in settlements to women who had accused "The O'Reilly Factor" host of sexual harassment, and after advertisers subsequently dropped the show en masse.

While working at Fox, Kasich occasionally served as a fill-in for O'Reilly on his program. Kasich filmed his show, "Heartland," from Columbus, Ohio.

"Well, look, I was there about seven years ago," he told Business Insider. "It was fine. If it wasn't fine, I wouldn't have stayed.

"There are changes going on. We'll see how it all works out," he continued. "I'm not in the management of Fox News. I think they're finding their way."

Last year, Roger Ailes, who was Fox News' chairman and CEO, resigned amid similar allegations of sexual harassment.

Kasich said he recently had a "private conversation" with James Murdoch, the CEO of 21st Century Fox and the younger son of Rupert Murdoch, the Australian-born media mogul who founded Fox News. Kasich, a onetime 2016 Republican presidential hopeful, did not expand on that conversation.

Watch part of Business Insider's interview with Kasich: