Republican presidential candidate and Ohio Gov. John Kasich said Friday that gay people are "probably" born that way, conceding that view during a testy exchange with a gay voter at a California event.

Asked by Kelly Bryan, a gay 62-year-old man, during an event at the Commonwealth Club of California whether people are "born gay," Kasich first attempted to avoid answering the question.

"I'm not gonna get into all the analysis of this or that," Kasich said at the San Francisco town hall. "I'm not gonna do that."

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But the questioner pressed again: "It's not analysis. Are people born gay?"

Kasich replied, "You know, sir, probably."

"I mean, I don't -- I don't know how it all works, OK?" he added. "I mean, look. Are they? You know, probability they are."

Asked whether the LGBT community deserved "free, regular rights like everybody else," Kasich said: "Well, you have free regular rights, we're not denying you any rights, I'm not in Ohio. I'm not out to discriminate against you. I think you ought to have as good a life as anybody else."

The Ohio governor also noted that he had recently attended a same-sex marriage ceremony.

"I don't agree with gay marriage," he said. "But I'm not -- I went to a gay wedding. OK? I mean, that's what I've done."

Earlier, Kasich had said, "A buddy of mine just got, you know, went, got married. My wife and I went to the wedding. It was great. It was fine. But I'm not going to go for some constitutional amendment."

When asked about Mississippi's and Kentucky's legislation allowing businesses to deny services to same-sex couples, Kasich suggested that he did not agree with them and argued that he has the "right to define the Republican Party too."

Defending his religious beliefs, Kasich had urged tolerance and mutual respect earlier in the night.

"Religion for me is about, you know, loving somebody that doesn't like you," he said. "Humility, love your neighbor as yourself, treat your spouse better -- you know, live a life bigger than yourself."

Kasich also made headlines at another California event later in the day, talking to reporters at the state's GOP convention in Burlingame about some Republican rhetoric concerning Latino voters.

"Do the Republicans actually think that they can win an election by scaring every Hispanic in this country to death?" Kasich said Friday. "Scaring them to the point where they're afraid their families are gonna be torn apart and disrupted? Do you have any idea what those folks are gonna do in the general election?"

Kasich weighed in on the anti-Donald Trump protests that broke out at the GOP convention earlier that afternoon.

"When you live on the, on the negative side, when you feed people's anger, did you see what happened here today?" Kasich asked. "I may not be winning those votes right now, but over time I believe that people like to live where they can be hopeful, where they believe that this country can be better -- where they believe at the end they need to have somebody that's had the experience and somebody that can unite the country."

CBS News' Erica Brown contributed to this report.