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Gov. John Kasich of Ohio, who has generally refrained from criticizing his presidential rivals, took on Donald J. Trump in a blunt manner on Thursday, declaring him “not prepared to be president.”

In an early-morning statement, Mr. Kasich cited Mr. Trump’s comments in the previous 24 hours about a variety of issues, including suggesting punishment for women who have abortions, which the businessman quickly recanted.

Mr. Kasich elaborated in interviews on morning television programs and at a news conference in Midtown Manhattan. On Fox News, he said that Mr. Trump was “all over the place” in his views, raising the use of nuclear weapons as one example.

“Are you kidding me?” Mr. Kasich asked. “How close is his thumb to the trigger? This is not the way you lead the United States, nor the way in which you lead the world.”

On ABC’s “Good Morning America,” Mr. Kasich used Mr. Trump’s recent comments as a reason to continue his presidential bid, even though his only way to win the Republican nomination would be at a contested convention.

“This is why I stay in the race,” he said. “Look, people say, ‘Why does he stay in the race?’ What, am I supposed to get out and leave it to these guys?”

As another example of an ill-conceived idea being advanced by his opponents, he brought up Senator Ted Cruz’s support for patrolling Muslim neighborhoods in the wake of last week’s terrorist attacks in Brussels.

“It’s either no record,” Mr. Kasich said, referring to Mr. Cruz, “or things that are coming out of Donald’s mouth that are just — they’re just basically irresponsible.”

The change in tone was striking because of the great extent to which Mr. Kasich has emphasized his positive message in recent months.

In limited ways, he has previously offered criticism of Mr. Trump, saying he had “created a toxic environment” and, this week, ridiculing his knowledge of foreign policy. But he has generally held back from laying into Mr. Trump, despite ample opportunity to do so, and he has warned that personally attacking Mr. Trump is not the way to beat him.

Asked at the news conference about his change in approach, he said he was “not going to live in this mode.”

“But when I see a number of these things that have been said, I have to say something about it,” he said. “If I don’t say something about it, then I really feel as though, as a public official, that I’m not doing my job.”

Mr. Kasich also made a direct appeal to voters who support Mr. Trump, saying that their frustrations “do not fall on deaf ears for me.”

Aside from offering harsh words for Mr. Trump on Thursday, Mr. Kasich defended himself after inciting his own controversy the day before: Visiting a pizzeria in Queens, he used a fork to eat some of a slice.

In the ABC interview, Mr. Kasich explained that the pizza was “scalding hot,” prompting him to use a fork. He joked that his wife said she was proud that he “finally learned how to use a utensil properly.”

He told reporters gathered in Midtown that he would do well in New York’s primary, which will be held April 19. (A Quinnipiac University poll released Thursday found Mr. Trump with the support of 56 percent of likely Republican primary voters, far ahead of Mr. Cruz, at 20 percent, and Mr. Kasich, at 19 percent.)

“Despite the fact that I got caught eating a piece of my pizza with a fork,” he said, “I think that we can overcome that.”