"Our enemies are going to take advantage of them," Mr. Kasich told voters near Cleveland. "Our friends are scratching their heads saying, 'What the heck is happening in America?' "
Mr. Kasich, who has boasted of bringing 400,000 jobs to Ohio and has visited businesses that opened under his watch, has marshaled nearly the entire elected Republican apparatus of Ohio.
On Monday, Mitt Romney, the 2012 Republican nominee who has been an outspoken critic of Mr. Trump, will appear with Mr. Kasich at two Ohio rallies.
Matt Borges, chairman of the state Republicans, warned that if Mr. Trump was the nominee, his divisiveness would cost Republicans the state in the general election. "If we don't carry Ohio in the fall, we don't elect a Republican to the White House," he said.
Mr. Trump's rally here was in West Chester, the hometown of John Boehner, the former House speaker who resigned last year out of frustration with the no-compromise wing of House Republicans. In a rare public appearance, Mr. Boehner endorsed Mr. Kasich at a county Republican dinner in West Chester on Saturday. The Trump rally on Sunday, just a few miles away, was attended by many hundreds more people.
"Kasich's done a great job with Ohio," said Doug Mason, a concrete laborer, but he still planned to vote for Mr. Trump. "I think Trump will be John Kasich on steroids."
The town-hall-style event for Mr. Trump was most notable for his response to a man who said it was important "for a lot of veterans in Ohio" that Mr. Trump clarify a comment, made last year, that former prisoners of war like Senator John McCain were not heroes.
"Oh no, no, no," Mr. Trump said. "They are real heroes."
— Reporting was contributed by Jeremy W. Peters from Largo, Fla.; Yamiche Alcindor from Affton, Mo.; Amy Chozick from Cleveland; Thomas Kaplan from Strongsville, Ohio; Matt Flegenheimer from St. Louis; Jonathan Martin from Washington; and Mitch Smith from Bloomington, Ill.