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COLUMBUS, Ohio — Arnold Schwarzenegger endorsed Gov. John Kasich on Sunday as Mr. Kasich rallied voters in his home state of Ohio, whose primary has emerged as a critical moment in the Republican race.

Mr. Schwarzenegger, wearing a jacket with the logo of the Kasich campaign at an outdoor rally here, told the crowd that Mr. Kasich “kicked some serious butt” during his time in Congress.

“He was an action hero when he went to Washington,” Mr. Schwarzenegger said.

Mr. Schwarzenegger, a former governor of California, puts on an annual sports festival in Columbus, which took place over the past few days. At the rally, he recalled being introduced to Mr. Kasich when he was first running for Congress in the 1980s, and cited his achievements in Congress and as Ohio’s governor.

“This is the land of opportunity; it is the greatest nation in the world, no matter what anyone says out there,” Mr. Schwarzenegger said. “And we need John Kasich to now take charge and be at the White House.”

Ohio’s winner-take-all primary, on March 15, is critical to Mr. Kasich as well as to efforts by Republican leaders to derail the candidacy of Donald J. Trump, whom Mr. Schwarzenegger happens to be replacing as the host of “The Celebrity Apprentice.”

Mr. Kasich hopes that a victory over Mr. Trump here will elevate him in the presidential race, allowing him to present himself as the best alternative. He has said he will leave the race if he does not win here.

Mr. Kasich urged the crowd to show that his positive approach to campaigning, avoiding what he described as “name calling” and “sliming,” can result in victory.

“I think it’s important that in Ohio, we not only send a message to the country, but we send a message to the world,” he said.