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HANOVERTON, Ohio — Mitt Romney, taking another step to counter Donald J. Trump, will join Gov. John Kasich of Ohio on Monday for two campaign stops as Mr. Kasich tries to win his home state.

The Ohio primary on Tuesday, a winner-take-all contest with 66 delegates, is a critical moment in the effort by Mr. Romney and other Republicans to stop Mr. Trump. Two recent polls have given Mr. Kasich an edge over Mr. Trump, but the contest is expected to be close.

Mr. Romney, who earlier this month denounced Mr. Trump, has suggested that voters support whichever candidate is the strongest alternative to Mr. Trump in their state. He is not expected to endorse Mr. Kasich when they appear together on Monday. Mr. Kasich has conceded that his campaign will have to end if he loses Ohio.

Last week, Mr. Romney recorded phone messages for Mr. Kasich and for Senator Marco Rubio of Florida. Florida’s primary is also on Tuesday, though Mr. Rubio has trailed Mr. Trump by a large margin there.

Mr. Kasich’s campaign said that Mr. Romney would join Mr. Kasich for an event between Canton and Akron, followed by one around Westerville, close to Mr. Kasich’s home in the Columbus area.

Ashley Parker contributed reporting from Boca Raton, Fla.