Combining Mr. Bannon's name with Breitbart, Mr. Scaramucci told ABC's George Stephanopolous, "You also got this sort of "Bannon-bart" influence in there, which I think is a snag on the president".
The president refused to express confidence in Bannon during an impromptu news conference Tuesday. "Sadly, it seems clear that influential members of his administration were more anxious about winning votes through dog whistles and winks and nods to the most evil elements of our society than in maintaining the moral authority of the presidency", U.S. Hispanic Chamber of Commerce CEO Javier Palomarez said in a statement issued Tuesday.
Trump's less-than-enthusiastic defense calls into question Bannon's assessment of his situation.
In his other comments to Kuttner, Steve Bannon "undercut the President's stance on North Korea", "openly talked about his internal fights with colleagues", and "talked about changing personnel in a way that made him sound like the president".
Richard Trumka, president of the AFL-CIO trade union federation, became the fifth prominent business leader to resign from Mr Trump's advisory body, the American Manufacturing Council, over the issue.
Bannon was a key general election campaign adviser and has been a forceful presence at the White House. The Fox News Channel remained loyal to Mr Trump's candidacy throughout his presidential campaign and hosted pundits who branded other news coverage Mr Trump "fake news".
While ousting Bannon might plug leaks targeting McMaster and Kushner, it sadly will not clear the white nationalists stench flowing out of the White House.
Bannon, the site's former executive chair, has called the Breitbart "a platform of the alt-right", referring to the small, deeply conservative movement that seeks a whites-only state.
In April, Trump diminished Bannon's role to that of "a guy who works for me". I went through 17 senators, governors and I won all the primaries. Bannon has denied being behind the anti-McMaster campaign.
"Ethno-nationalism - it's losers", he said. Among them are Jared Kushner and Ivanka Trump, family members and top White House employees.
"We're at economic war with China", Bannon told Kuttner.
Over the last few days, there has been an increasing demand to fire Mr. Bannon with critics labelling him as a white supremacist.
He has told associates that he has no plans to leave the White House and would only do so if Trump fires him.
That approach is lifted from a playbook he's already had to use.
Bannon's strategy, according to Kuttner, "is to battle the trade doves inside the administration while building an outside coalition of trade hawks that includes the left as well as right". The blowback to the botched introduction of the ban, which was rolled out quickly with little outside consultation, angered many in the administration, including Kelly, then head of Homeland Security. This week has brought a flurry of news reports that Bannon is on thin ice.
Bykowicz reported from Washington.