Mr. Priebus and Stephen K. Bannon, the president’s chief strategist, both strongly opposed the appointment of Mr. Scaramucci — in large part because he enjoys an easy banter and direct line to Mr. Trump, potentially threatening their positions, four people briefed on the discussions said. People close to both men insisted they had not opposed the move by the president.

Mr. Trump, aggravated by their opposition, dressed the pair down in a testy Oval Office exchange around the time he decided to offer Mr. Scaramucci — known in Trump’s circle as “The Mooch” — the job.

The president, according to three people with knowledge of the situation, said one of the reasons he hired Mr. Scaramucci was to cut down on anonymous leaking — and took a swipe at his two advisers…

In recent weeks, Mr. Trump had told people that Mr. Spicer was no longer “tough,” one of the harshest insults he can level. And Mr. Spicer told friends he was tired of being blindsided by Mr. Trump, and weary of Mr. Trump’s constant criticism. He instituted the highly contentious practice of holding off-camera briefings, less so to snub reporters than to avoid Mr. Trump’s critiques of his performance, according to one of Mr. Spicer’s friends.