The statement from the president came after the release of explosive excerpts from a new book about the Trump White House, in which Bannon describes a meeting between Trump's son Don Jr and a Russian lawyer during the 2016 presidential election campaign as "treasonous" and "unpatriotic."
"Steve Bannon has nothing to do with me or my presidency. When he was fired, he not only lost his job, he lost his mind," Trump said in a statement that was notably abrasive, even for America's combative 45th president.
Trump said Bannon -- who engineered the New York real estate mogul's link to the nationalist far right and helped create a pro-Trump media ecosystem -- was "only in it for himself."
The book -- the "Fire and Fury: Inside the Trump White House," by journalist Michael Wolff -- is to be published next week.
But both The Guardian and New York magazine released excerpts that also touch on the presidential ambitions of Trump's daughter Ivanka -- and which say that Trump himself did not believe he would defeat Clinton.
Bannon, who left the White House in August, is also quoted as saying that the investigation by special counsel Robert Mueller into Russian interference in the 2016 election will focus on money laundering.
The investigation by Mueller, a former FBI director, is looking into whether the Trump campaign colluded with Russia to get him elected -- a charge the president has repeatedly and vehemently denied.
'You should have called the FBI'
Don Jr took the June 9, 2016 meeting with Russian lawyer Natalia Veselnitskaya after an intermediary promised material that would incriminate Trump's Democratic rival Hillary Clinton.
Trump's son-in-law Jared Kushner and then campaign chairman Paul Manafort also attended the meeting at Trump Tower in New York.
"Even if you thought that this was not treasonous, or unpatriotic, or bad shit, and I happen to think it's all of that, you should have called the FBI immediately," he said.
'Little to do' with election win
Trump responded quickly and cuttingly to the reported comments by Bannon, a former investment banker and the executive chairman of influential ultraconservative outlet Breitbart News.
"Now that he is on his own, Steve is learning that winning isn't as easy as I make it look. Steve had very little to do with our historic victory, which was delivered by the forgotten men and women of this country," Trump said.
"Steve pretends to be at war with the media, which he calls the opposition party, yet he spent his time at the White House leaking false information to the media to make himself seem far more important than he was," he added.
"Steve was rarely in a one-on-one meeting with me and only pretends to have had influence to fool a few people with no access and no clue, whom he helped write phony books."
Wolff's book -- which he says is based on interviews with Trump, his senior aides and others -- also mentions that Trump did not initially know who former House speaker John Boehner was, and that he eats food from McDonald's because he believes it to be safe.
"This book is filled with false and misleading accounts from individuals who have no access or influence with the White House," said Trump's press secretary Sarah Sanders.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)