"I don't believe there's any way back for Mr Bannon at this point. It is very obvious that Mr Bannon worked with Mr Wolff in this particular book," White House Deputy Press Secretary Hogan Gidley told reporters aboard Air Force One.
He was responding to a question on the statement by Bannon a day earlier in which he had apologised for his critical remarks in the book 'Fire and Fury: Inside the Trump White House' by Michael Wolff.
In a statement, Trump said Bannon has nothing to do with his presidency and has "lost his mind".
"The President has been very clear on his thoughts; issued a four-paragraph statement about Mr Bannon. Zero ambiguity in those statements. It was obvious that the book was false and fake," Gidley said.
"When you go after somebody's family, in the manner in which he did -- two of the President's children who are serving this nation, sacrificing in their service -- it is repugnant, it is grotesque.
"And I challenge anybody to go and talk about someone else's family and see if that person doesn't come back and come back hard," Gidley said.