“Any insinuation to the contrary is purely overblown gossip,” Mr. Priebus said.

And Jason Miller, Mr. Trump’s spokesman, said: “Cooperation between the Trump campaign and the R.N.C. has never been better — we are fully integrated. Everybody knows what has to be done to elect Mr. Trump and stop Hillary Clinton.”

But senior advisers to Mr. Priebus and Mr. Trump have collided over the turbulence in the campaign, the senior Republicans said. Mr. Trump’s top policy adviser questioned Mr. Priebus’s competence in a caustic email this week after the Phoenix speech. And Mr. Trump’s son-in-law, Jared Kushner, and Mr. Priebus’s chief of staff clashed in a tense meeting over the use of the committee’s war chest.

Within Mr. Trump’s circle, there is impatience with what advisers view as a cautious and conventional party bureaucracy, ill-equipped to accommodate Mr. Trump’s improvisational style. At times, Trump aides have vented that frustration in language that was contemptuous of Mr. Priebus, a genial Wisconsin lawyer who has been chairman for five years.

When Mr. Trump’s immigration speech this week spurred resignations from the National Hispanic Advisory Council for Trump, a party-backed group, one of Mr. Trump’s top advisers lashed out at Mr. Priebus in an email to the campaign staff.

“The RNC needs to take control of this situation and quickly,” wrote Stephen Miller, Mr. Trump’s senior policy adviser, who often travels with the candidate.

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Describing the Hispanic Republicans who resigned in dismay as “professional amnesty lobbyists,” Mr. Miller asked, “Can Reince do his job?”

Inside the committee, top officials have lost confidence in Mr. Trump’s ability to right his listing campaign, according to the senior Republicans. Complaints abound about the haphazard nature of Mr. Trump’s operation, in which power is so divided among strategists and members of the Trump family that the process of making even simple decisions is laborious and unpredictable. Mr. Trump is on his third campaign leadership team, having dismissed two previous chief advisers, and he has already fired two senior staff members, Rick Wiley and Ed Brookover, whose jobs included coordinating his strategy with the R.N.C.

Mr. Priebus, who has a warm relationship with Mr. Trump and speaks with him daily, has also confided to some Republicans that he has been disappointed by Mr. Trump’s failure to evolve as a candidate in the general election.

He denied in a statement that he had complained about Mr. Trump’s refusal to shift course. “I’ve said exactly the opposite,” Mr. Priebus said. “I think he’s had his best three weeks.”

Robin Hayes, the chairman of the North Carolina Republican Party, said he was optimistic about the emerging relationship between his organization and the Trump campaign in his own state. But Mr. Hayes said it was widely understood within the national committee that Mr. Trump needed to make adjustments.

“There have been discussions, that we don’t need to create, ‘Cleanup on Aisle 3,’ for ourselves,” Mr. Hayes said. “He’s still going to be Trump — that’s important — but Trump in a way that fits into a general election.”

Throughout the campaign, Mr. Priebus and his committee have been broadly deferential to Mr. Trump, declining to criticize many of his most provocative remarks and quickly designating him as the party’s presumptive nominee in May. For Mr. Trump, Mr. Priebus has appeared to be a patient and accommodating partner, eager to promote his campaign and willing to rebuke Republicans who have declined to support him.

Recently, the committee has sent aides to work several days a week at Trump Tower to bolster collaboration with Mr. Trump’s campaign. These include Sean Spicer, a close adviser to Mr. Priebus.

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But the conflict has continued. At a meeting in New York late last month, Mr. Kushner, who is married to Ivanka Trump, pointedly challenged Katie Walsh, the committee’s chief of staff, over the party’s spending plans.

ADVERTISEMENT Advertisement Continue reading the main story In a tone that several witnesses described as imperious and aggressive, Mr. Kushner suggested that the national committee might not be giving Mr. Trump all the support he was due.

Ms. Walsh pushed back strongly, telling Mr. Kushner, who has no background in politics, that the committee’s fund-raising and spending are disclosed in detail to the Federal Election Commission, according to the witnesses who were in the room and two people briefed by them afterward.

Ms. Walsh told Mr. Kushner that the committee had a responsibility to take a broad view of its finances, mapping out a budget for the entire party and ensuring it could remain operational for the rest of the year, and could not solely focus on Mr. Trump’s needs.

Mike DuHaime, a former political director for the committee, said tensions with the campaign could be harmful to both sides in the general election.

“For the field operation to be truly effective, the campaign, the R.N.C and down-ballot races need to be on the same page about goals and resource allocation,” he said.

Rudolph W. Giuliani, the former New York City mayor who has become one of Mr. Trump’s closest advisers, said he was confident that Mr. Priebus remained “on board” with the Trump campaign. At the same time, he acknowledged that much of the institutional Republican Party remained unfriendly to Mr. Trump.

“The R.N.C. is giving him a lot of support,” Mr. Giuliani said. “He doesn’t have the united Republican Party behind him in the way that a more establishment candidate would.”