Fired White House communications director Anthony Scaramucci has also signaled discord with Bannon in his own appearance on ABC's "This Week".
Scaramucci's frustration with Bannon was put on full display last month after New Yorker reporter Ryan Lizza published an article detailing an expletive-laced phone conversation he had with Scaramucci. "With the moral authority of the presidency, you have to call that stuff out".
He said the "toleration of [white supremacy] by Steve Bannon is inexcusable".
"He has to moved away from that sort of Bannon-bart nonsense", Scaramucci added.
The Trump White House reportedly received another, "Thanks, but no thanks" response from a high-profile player who has passed on a senior administration position.
The power struggle between McMaster's camp and the White House's more nationalist faction, led by chief strategist Steve Bannon, was highlighted in a memo obtained by Foreign Policy.
"I think that there are elements inside of Washington, also inclusive in the White House, that are not necessarily abetting the president's interests or his agenda", the Manhasset financier told ABC News' "This Week".
He said that if he was still working in the White House, he would not have recommended Trump make the statement he did.
When asked by Stephanopoulos if that influence stemmed from Bannon, Scaramucci said, "I think the president knows what he's going to do with Steve Bannon".
He said it was hard for White House aides to change Trump's thinking, but that those around him needed to "be blunt with him".
Asked about the call on This Week Sunday morning, Scaramucci said "the words were mischaracterized in the original article", before noting that Lizza is "not misquoting me, but he is mischaracterizing me".