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GREEN, Ohio — Mitt Romney, in his latest attempt to help stop Donald J. Trump, joined Gov. John Kasich of Ohio on the campaign trail on Monday as Mr. Kasich tries to pull out a victory in his home state.

At an air museum between Akron and Canton, where Mr. Kasich’s campaign bus pulled in next to a World War II-era bomber, Mr. Romney highlighted Mr. Kasich’s experience in Congress and as Ohio’s governor.

“Unlike the other people running, he has a real track record,” Mr. Romney said in introducing Mr. Kasich at the town hall style event. “He has the kind of record that you want in Washington, and that’s why I’m convinced that you’re going to do the right thing tomorrow.”

In remarks lasting under four minutes, Mr. Romney did not mention Mr. Trump, nor did he give an explicit, broad endorsement of Mr. Kasich. But he came close; saying that “America is looking to Ohio to do a job interview,” he told voters that Mr. Kasich was “the guy that Ohio needs to vote for.”

“America’s counting on you,” Mr. Romney said.

Afterward, Mr. Kasich observed, “How things would have been different if the election results had been different four years ago, huh?”

Mr. Kasich said it was “so nice of Mitt to come out and support me here in this effort to win this state.” He went on to highlight and praise Mr. Romney’s work on the 2002 Winter Olympics, which he said had been “falling apart.”

He said that the Olympics could have been a global embarrassment, one that would have been almost “as bad as people slugging it out at a campaign rally,” a reference to the violence at Mr. Trump’s rallies.

Mr. Kasich, who has accused Mr. Trump of creating a “toxic environment,” asked the audience to “think of the images that have been broadcast across this world of the way we’re picking a president here.”

“You think they’re not using that for propaganda, to send a message to people that America’s broken?” Mr. Kasich asked.

Mr. Romney’s appearances with Mr. Kasich seemed to carry the risk of putting off some voters. Mr. Romney’s intervention in the Republican race this month, and his instructions to voters to stop Mr. Trump, drew contempt from some rank-and-file Republicans.

There was evidence of that reaction as Mr. Kasich campaigned on Monday.

At an earlier event in Youngstown that did not include an appearance by Mr. Romney, Adam Rutushin, a retired pharmacist who is running for county office, brought up Mr. Romney, and not in a positive way.

Mr. Rutushin supports Mr. Kasich, but expressed disappointment in Mr. Romney, saying before the event that he did not like his asserting himself in the race. “The important thing is that the people choose,” he said. “It shouldn’t be engineered.”

Before the event here, another Kasich supporter, Carole Miller, a retired schoolteacher, said Mr. Romney could help Mr. Kasich’s chances in Tuesday’s primary. But she was not eager for Mr. Romney to play a lasting role in the presidential race.

“I think it’ll be helpful for Kasich,” she said. “Then he should butt out.”

Even Mr. Kasich himself has showed some hesitance. Last week, he distanced himself from a get-out-the-vote call that Mr. Romney recorded for the Kasich campaign, which focused on undermining Mr. Trump.

But he welcomed Mr. Romney’s help on Monday.

“He’s going to come in and be positive,” Mr. Kasich told reporters in Youngstown. “He’s going to talk about me. I don’t expect he’s going to come in here and be trashing anybody. We don’t want that.”

Mr. Kasich noted that his second event with Mr. Romney, scheduled for Monday evening, was near his home in the Columbus area.

“Who knows?” Mr. Kasich said. “If we have enough time, maybe I’ll even take him to my house and show him, you know, show him where I live.”