The interview comes hours after Scaramucci copied Priebus in a tweet about leaks, later deleted the tweet and then told CNN -- before his interview -- that the message was not a call for the FBI to investigate the chief of staff.
Scaramucci, whose relationship with Priebus has been fraught since he was initially unable to secure a White House job after President Donald Trump's election, did little to show his relationship with Priebus was changing and said it was up to the chief of staff to show he was not leaking.
"When I put out a tweet and I put Reince's name in a tweet, they're all make the assumption that it's him because journalists know who the leakers are," Scaramucci said. "So if Reince wants to explain he's not a leaker, let him do that. But let me tell you about myself. I'm a straight shooter and I'll go right to the heart of the matter."
Scaramucci also blasted leakers in the administration and said "the President and I would like to tell everybody we have a very, very good idea of who the leakers are, who the senior leakers are in the White House."
Scaramucci, in his first appearance in the White House briefing room last week, said he and Priebus were like brothers who fought at times. In Thursday's interview with CNN, he compared the relationship to that of Cain and Abel, the biblical sons of Adam and Eve. According to the Book of Genesis, Cain murdered Abel and later lied about his actions.
"Now, if you want to talk about the chief of staff, we have had odds, we have had differences," he 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 repairable or not. That will be up to the President."
Then, referring to leaks about US foreign policy, Scaramucci said, "Those are the types of leaks that are so treasonous that 150 years ago, people would have actually been hung for those types of leaks."
After Politico published a story about how the he continues to profit from the sale of his hedge fund SkyBridge Capital, Scaramucci slammed the leak of his Office of Government Ethics forms.
"In light of the leak of my financial disclosure info which is a felony. I will be contacting @FBI and the @TheJusticeDept, he tweeted Wednesday night, adding, "#swamp @Reince45."
The inclusion of Reince in the tweet was seen by some as an accusation.
The financial disclosure forms, however, are publicly available, notes the Politico report, which links to them. CNN has not independently obtained the disclosure form.
Asked if he was accusing Priebus of leaking before his interview on "New Day," Scaramucci told CNN, "I am not. I am saying senior officials are working on this together."
This echoes a tweet he sent overnight as well.
"Wrong! Tweet was public notice to leakers that all Sr Adm officials are helping to end illegal leaks.@Reince45," he tweeted in response to an Axios article's headline that read, "Scaramucci appears to want Priebus investigated by FBI."
Scaramucci and Priebus have long had a strained relationship, but Thursday's interview is the most public airing of that relationship yet. Sources have told CNN that both Priebus and chief strategist Steve Bannon fiercely opposed Scaramucci's hiring as communications director.
When he joined the administration late last week, Scaramucci pushed back on reports of any discord inside the West Wing, especially about the reports of a tense relationship with Priebus.
"Reince and I have been personal friends for six years," Scaramucci said Friday. "We are a little bit like brothers where we rough each other up once in a while. But he's a dear friend."
Still, Scaramucci said he would report "directly" to the President, and that he and Priebus would work together.
CNN's Eugene Scott contributed to this report.