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DETROIT — Gov. John Kasich of Ohio on Thursday echoed calls to derail Donald J. Trump, and he predicted that if he won his home state, the Republican nomination would be decided at the party’s convention in July.

“I think it is important that we stop Mr. Trump,” Mr. Kasich said at a news conference at a hotel here in Michigan, which has its primary on Tuesday.

The Ohio primary is March 15, as is the primary in Florida, the home state of Senator Marco Rubio. Both are winner-take-all contests, and they loom as pivotal moments for Republicans seeking to stop Mr. Trump from clinching the nomination by winning a majority of delegates before the convention.

“At the end of the day in all this, it is going to get down to a couple states, and Ohio is going to be absolutely critical,” Mr. Kasich told reporters. “And we will go all out, and I will win Ohio.”

“If in fact I win Ohio, then we’re going to probably go to a convention,” he added. “That’s what it looks like. And it’s going to be the most exciting time.”

Mr. Kasich said he understood why voters, filled with angst and frustration, were drawn to Mr. Trump. But, referring to Mr. Rubio’s approach in recent days, he warned that “you don’t beat Trump by personal attacks.”

“I just don’t want to go and talk about the size of his hands, or what kind of a tan he has,” Mr. Kasich said. “That’s not the way to get this done.”

Mr. Kasich said he had expressed that view to Mitt Romney. On Thursday, Mr. Romney suggested that voters should support whichever candidate was strongest against Mr. Trump in a given state, such as Mr. Rubio in Florida and Mr. Kasich in Ohio. But Mr. Kasich, while expressing appreciation for Mr. Romney’s suggestion that people in Ohio vote for him, did not endorse that plan of action.

Asked if he wanted his supporters in Florida to vote for Mr. Rubio, Mr. Kasich responded, “Right now, I think they ought to vote for me.”

Mr. Kasich said that if the nomination were to be decided at the convention, he would become the nominee. And he playfully took note of the gathering’s location: Cleveland.

“I don’t know whether you noticed or not, it’s being held in Ohio,” the governor said. “We plotted this all out.”