WASHINGTON — The internal rivalries of the White House spilled out into stark public view on Thursday as President Trump’s new communications director publicly attacked the chief of staff, calling him a “paranoid schizophrenic” leaker and vowing to get him fired.

Anthony Scaramucci, who was installed as White House communications director last week over the objections of the chief of staff, Reince Priebus, in the morning called into CNN to say that the two men were at odds and to dare Mr. Priebus to deny being a leaker. By the evening, The New Yorker had posted an interview quoting Mr. Scaramucci using vulgar language to describe Mr. Priebus.

“Reince Priebus — if you want to leak something — he’ll be asked to resign very shortly,” Mr. Scaramucci told The New Yorker’s Ryan Lizza in an angry, profanity-laced telephone call on Wednesday night. Mr. Scaramucci suggested that he believed that Mr. Priebus was leaking information to damage him. “Reince is a fucking paranoid schizophrenic, a paranoiac,” he said.

The Run-Up

The podcast that makes sense of the most delirious stretch of the 2016 campaign.

In the same telephone call, Mr. Scaramucci disparaged Stephen K. Bannon, the president’s chief strategist, who also warned against hiring him as communications director. “I’m not Steve Bannon. I’m not trying to suck my own cock,” he said. “I’m not trying to build my own brand off the fucking strength of the president. I’m here to serve the country.”

Mr. Scaramucci later released a statement but did not apologize. “I sometimes use colorful language,” he said on Twitter. “I will refrain in this arena but not give up the passionate fight for @RealDonaldTrump’s agenda.”

Sarah Huckabee Sanders, the new White House press secretary, said she had nothing to add to the statement. Mr. Priebus and Mr. Bannon had no immediate comment.

The phone call underscored the depth of divisions within the West Wing, which have only widened with Mr. Scaramucci’s arrival. Not only did Mr. Priebus and Mr. Bannon oppose his appointment, but Sean Spicer resigned as press secretary in protest.

Mr. Scaramucci was angry about what he saw as leaks targeting him. Mr. Lizza had posted a message on Twitter on Wednesday night reporting that Mr. Trump and Mr. Scaramucci were having dinner at the White House with Sean Hannity, the Fox News host and a strong supporter of the president, and Bill Shine, a former Fox executive. Mr. Scaramucci called Mr. Lizza unsolicited to demand that he identify his source.

When Mr. Lizza would not, Mr. Scaramucci said, “O.K., I’m going to fire every one of them, and then you haven’t protected anybody, so the entire place will be fired over the next two weeks.”

Mr. Scaramucci was also mad about a story on Politico reporting his financial disclosure form. In a Twitter post on Wednesday night shortly after his conversation with Mr. Lizza, Mr. Scaramucci said the “leak” was “a felony” and that he would be contacting the F.B.I. and Justice Department to seek an investigation. He then included Mr. Priebus’s Twitter handle, which several officials in the White House interpreted as meaning that he suspected the chief of staff.

On Thursday morning, he telephoned into CNN and agreed that he was at loggerheads with Mr. Priebus, comparing them to Cain and Abel, the biblical sons of Adam and Eve whose conflict led to Cain murdering Abel. He challenged Mr. Priebus to deny being a leaker.

“We have had odds. We have had differences,” Mr. Scaramucci said. “When I said we were brothers from the podium, that’s because we’re rough on each other. Some brothers are like Cain and Abel. Other brothers can fight with each other and get along. I don’t know if this is reparable or not. That will be up to the president.”

But the leak he was complaining about was no leak. Lorraine Woellert, Politico’s reporter on the story, explained that she simply requested the financial disclosure form through normal channels and was provided it by a government agency as required by federal law. Mr. Scaramucci deleted his Twitter message but posted a new one referring to a story by the news outlet Axios suggesting that he wanted Mr. Priebus investigated.

As the hosts and guests of CNN’s “New Day” discussed the matter on Thursday morning, Mr. Scaramucci called in to address the question of Mr. Priebus.

“He’s the chief of staff,” he said. “He’s responsible for understanding and uncovering and helping me do that inside the White House, which is why I put that tweet out last night.” The fact that journalists interpreted it as an accusation against Mr. Priebus suggested that he might be a leaker because the journalists know who gives them information, Mr. Scaramucci said.

“When I put out a tweet and I put Reince’s name in the tweet, they’re all making the assumption that it’s him because journalists know who the leakers are,” he said. “So if Reince wants to explain that he’s not a leaker, let him do that. Let me tell you something about myself. I am a straight shooter and I’ll go right to the heart of the matter.”

The disclosure form, filed with the Export-Import Bank, where Mr. Scaramucci worked briefly before joining the White House, showed that he has assets worth as much as $85 million. He made $5 million in salary and another $4.9 million from his ownership stake in his investment firm SkyBridge Capital in the first six months of this year, according to the filing.

Under federal law, disclosure forms are publicly available and agencies that receive them have 30 days to open them to the public. Mr. Scaramucci’s report says it was filed on June 23, which meant that it had to be available for release by the bank by July 23, this past Sunday.