Mitt Romney’s bid for Utah’s open U.S. Senate seat isn’t official yet, but it’s already shaping up to be deeply divisive for the Republican Party.

Utah Republican Party Chairman Rob Anderson called Mr. Romney a carpetbagger who is out of touch with the state’s conservative voters and at odds with the party’s leader, President Trump.

“I think he’s keeping out candidates that I think would be a better fit for Utah because, let’s face it, Mitt Romney doesn’t live here, his kids weren’t born here, he doesn’t shop here,” Mr. Anderson told The Salt Lake Tribune.

Mr. Anderson also aired concerns that Mr. Romney “has never been a Trump supporter.”

The criticism sapped some of the energy Mr. Romney and his allies were trying to build around his bid for the seat of Sen. Orrin G. Hatch, the Senate’s most senior Republican, who is retiring at the end of this year.

Mr. Romney, 70, the 2012 Republican presidential nominee, lost what party leaders thought would be a winnable election.

He had been planning to enter the Senate race on Thursday via social media, joining a Republican primary field that includes Chris Forbush, Timothy Jimenez and Larry Meyers.

But on Wednesday evening, with the nation grieving in the wake of 17 dead in a school shooting in Florida earlier in the day, Mr. Romney announced he would postpone the official launch.

“Out of respect for the victims and their families, I will not be making an announcement tomorrow about the Senate race,” he said in a statement.

If Mr. Romney wins the party’s nomination, he could create problems for the Republican National Committee, which is chaired by Mr. Romney’s niece, Ronna Romney McDaniel, but takes its marching orders from Mr. Trump and the White House.

The New York Times and other news outlets reported that Mrs. McDaniel stopped using the Romney name after Mr. Trump jokingly suggested that she would be better off without it in her professional life.

The RNC did not respond to multiple inquiries about how it would approach Mr. Romney’s candidacy.

Thomas Wright, an RNC member from Utah, said the committee supports its candidates and expects that to be the case if Mr. Romney captures the nomination.

“I have always said in politics that it is healthy to have disagreements to vigorously debate issues, to have other people’s points of view and then to come together,” Mr. Wright recently told The Washington Times. “I have no doubt that that will continue to happen in Utah.”

Others said RNC support doesn’t matter because Mr. Romney has a national data operation, high approval ratings and all the resources he will need to win the race.

Mr. Romney, a Mormon, won more than 72 percent of the vote in Utah in the 2012 election. Mr. Trump won 46 percent of the Utah vote in 2016.

Boyd Matheson, who served as chief of staff for Sen. Mike Lee, Utah Republican, and considered running for the Hatch seat earlier this year, said he doesn’t expect a lot of fireworks between Mr. Trump and Mr. Romney.

“I think the one thing that Mitt Romney understands about President Trump is that President Trump is 100 percent transactional,” Mr. Matheson said. “People who hate Donald Trump and expect Mitt Romney to go after him in a cage match are going to be disappointed, and the people who hate Mitt Romney and want the president to go after him in a cage match are going to be disappointed.”

Given the two men’s history, some fireworks may be expected.

Mr. Trump endorsed Mr. Romney’s presidential campaign in 2012, but their relationship soured in 2016 when Mr. Romney delivered a speech to call the New York Republican a “phony” and a “fraud.”

Mr. Trump countered that Mr. Romney was a “stone-cold loser” and a “real stiff.”

Kevin Madden, a Republican Party consultant who worked on Mr. Romney’s 2012 campaign, said Mr. Romney is running to be one of 100 senators. If he wins, Mr. Madden said, his first duty is to be a good ambassador for the people of Utah — not the face of the anti-Trump Republican Party.

“That doesn’t mean when he sees areas where he has to speak out and I think maybe guide the policy conversation or political conversation in a direction where he thinks the president is doing the wrong thing, he will certainly take the opportunity as he has shown time and time again,” Mr. Madden said.

The momentum behind a Romney bid picked up speed in January after Mr. Hatch announced his retirement and urged Mr. Romney to run for the seat. Around the same time, Mr. Romney changed the location on his Twitter profile from Massachusetts to Holladay, Utah.

Some Republicans have high hopes for Mr. Romney and suggest he could be a leader in the upper chamber.

“Were he to enter the Senate, he would not be a typical freshman senator,” said Utah Gov. Gary Richard Herbert, a Republican.

Still, it is clear that some Republicans, including Mr. Anderson, the state party chairman, are not sold.

“I have two questions for Mitt. First of all, why?” Mr. Anderson said. “And how do you expect to represent Utah when you don’t live here?”

The comments shocked Dave Hansen, a former state party chairman.

“I can’t think of a logical reason why he would do that,” Mr. Hansen said. “This is out of the clear blue.”

Mr. Hansen said the race is all but over once Mr. Romney joins.

“Romney is going to win,” Mr. Hansen said.

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