WASHINGTON — Anthony Scaramucci, President Trump’s new communications director, vowed on Tuesday to purge the White House staff of disloyal aides in an effort to crack down on leaks, as another member of the press staff resigned from a West Wing reeling from an unfolding shake-up.

“I’m going to fire everybody — that’s how,” Mr. Scaramucci told reporters in the White House driveway, when asked how he planned to identify who had been disclosing information to reporters without authorization and ensure that the leaks stopped. He said he had authority directly from Mr. Trump to do so.

“You’re either going to stop leaking, or you’re going to get fired,” he said.

“If I’ve got to get the thing down to me and Sarah Huckabee, then the leaking will stop,” he added, referring to Sarah Huckabee Sanders, the newly named press secretary who stepped in after Sean Spicer resigned last week in protest of Mr. Scaramucci’s hiring.

Michael C. Short, an assistant press secretary who had been close to Mr. Spicer, resigned just hours after Mr. Scaramucci had been quoted in a news report saying he would be fired, according to a person familiar with the matter who insisted on anonymity to discuss a personnel matter.

His departure marked another setback for Reince Priebus, the White House chief of staff and former chairman of the Republican National Committee, who populated the West Wing with a group of former R.N.C. aides loyal to him. Those affiliated with the establishment forces of the party are often viewed with suspicion by others in Mr. Trump’s inner circle.

Both Mr. Priebus and Mr. Spicer had argued forcefully against bringing on Mr. Scaramucci, whose hiring seemed to signal a pivot by the White House toward surrounding Mr. Trump with people more likely to stick by the campaign coda of “let Trump be Trump.” Mr. Trump has long been suspicious of the party committee hires, whose personal loyalty he has repeatedly questioned.

The targeting of Mr. Short — coupled with Mr. Trump’s increasingly bitter public feud with his attorney general, Jeff Sessions, one of his earliest and most loyal campaign supporters — put staff aides throughout the White House on edge on Tuesday, with several expressing concern about their jobs and lamenting an increasingly toxic atmosphere.

Mr. Trump has been plagued since taking office by a leaky White House, where warring factions of aides and advisers have routinely litigated their internal disputes in the press, leading to unflattering disclosures about senior members of Mr. Trump’s team and the president himself. Mr. Scaramucci’s threats appeared intended to reassure Mr. Trump that he would do something to solve the problem, although there is little evidence that the deep rifts within his inner circle have been resolved.

Mr. Scaramucci conceded that the leaking was not confined to the communications operation.

“There are leakers in the comms shop, there are leakers everywhere,” Mr. Scaramucci said, calling the practice atrocious, outrageous and unpatriotic. “It damages the president personally, it damages the institution of the presidency, and I don’t like it.”

Behind the scenes, Mr. Scaramucci has struck a gentler tone, telling colleagues in a meeting on Monday that their contributions were appreciated and he wanted everyone to work together to improve how the White House functioned. But he presented few details about his plans for changes in the coming days.

On Tuesday, he told reporters he would apply the no-leaks policy in the future, forgiving past unauthorized disclosures as long as the practice ceased.

“If they don’t stop leaking, I’m going to put them out on Pennsylvania Avenue,” Mr. Scaramucci said, gesturing at the street outside the White House gates with his eyes shielded from the sun by blue-tinted aviator sunglasses. ” Do you want to sell postcards to the tourists outside the gate, or do you want to work in the West Wing. What do you want to do?”

Yet what prompted his broadside against leaks was a question from a reporter about the fate of Mr. Short, whom Mr. Scaramucci himself had told Politico earlier on Tuesday was to be dismissed.

“Let’s say I’m firing Michael Short today,” he said when asked about the story, hours before Mr. Short quit. “The fact that you guys know about it before he does really upsets me as a human being and as a Roman Catholic. I should have the opportunity, if I need to let somebody go, to let the person go in a very humane, dignified way.”