CLEVELAND — Ohio Gov. John Kasich is a man about town in and around Cleveland this week, making the rounds of the delegations to the Republican National Convention, but he’s deliberately shied away from the man of the hour — Donald Trump.

Holding court a stone’s throw from the arena where Mr. Trump will be formally nominated, Mr. Kasich on Monday praised police officers, asked Republicans to support down-ballot candidates and promoted his own criminal justice and education record in Ohio, saying it was evidence of Republicans’ “big tent” philosophy.

“We don’t want to cut anybody out,” he said.

Yet Mr. Kasich’s tent doesn’t appear big enough for Mr. Trump — a sore point for party officials running the convention. Mr. Trump’s campaign chairman said the governor is “embarrassing” his state, and Ohio’s delegation was relegated to the back corner of the convention floor.

Mr. Kasich was the last of 16 GOP primary challengers to admit defeat to Mr. Trump this year, and he’s still refusing to endorse the unpredictable mogul or even be seen with him.

For one thing, the governor didn’t think it would come to this point, predicting in March that Mr. Trump would never amass enough delegates to secure the nomination. But then he did, and the “Never Trump” movement gasped its last breath on the convention floor Monday.

The upshot is that Mr. Trump and his team must launch the nominee’s race to November without the help of the host state’s Republican governor.

“We invited him; we wanted him to participate. He chose not to,” said Paul Manafort, the Trump campaign chairman.

Some Ohioans at the convention were willing to give their governor a pass on holding out.

“We love our governor, he’s a terrific guy,” said Jim Dicke, an Ohio delegate, as the convention gaveled in for first-day festivities.

Others say it is time for Mr. Kasich to make good on the vow he made to support the eventual nominee.

“It may take him a little bit longer than others, but I think it’s important that he honor his pledge and support our nominee,” said Aaron Del Mar, an at-large delegate from Cook County, Illinois. “Because we all need to be united going into November to defeat Hillary Clinton.”

The governor’s campaign team said Sunday he will spend his time at events in and around Cleveland this week with delegations from Illinois, Michigan, Pennsylvania and New Hampshire instead of playing a prominent role in floor festivities.

Four years ago, Republican Gov. Rick Scott also missed much of his party’s festivities in Tampa, Florida. But that was because of a looming hurricane, not because he didn’t like 2012 nominee Mitt Romney.

Mr. Kasich told NBC News that for him to speak at this year’s event, Mr. Trump would have to “change everything that he says.”

“We can’t be attacking Muslims and Hispanics, and trying to shut down trade, and not caring about the debt. Those are all problems for me,” he said.

Political analysts say Mr. Kasich’s boycott of Trump-related fare is indicative of a bitter and unpredictable election year. Some top Republicans are doing everything they can to protect the GOP’s House and Senate majorities on Capitol Hill, even as they shy away from the man at the top of the ticket.

“The state party desperately wants to re-elect Sen. Rob Portman [of Ohio], and they may need optimal Republican turnout in order to do that. So Trump, Kasich and the state party may eventually need each other. But it is an odd circumstance indeed that the popular governor of Ohio wants nothing to do with his own party’s convention in his home state,” said Kyle D. Kondik, managing editor of Sabato’s Crystal Ball and author of a recently released book titled, “The Bellwether: Why Ohio Picks the President.”

• David Sherfinski contributed to this report.

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