The letter from lawyer Charles Harder, dated Thursday, comes after excerpts of Wolff's book have cast the president and much of his White House in an unflattering light, portraying the commander-in-chief as someone who does not understand constitutional amendments, and is sometimes not taken seriously by key advisers.
Identifying "mental stability" and being "really smart" as his two greatest assets, Trump in a series of tweetssaid that winning the presidential election on his first attempt qualifies him as a "genius". "I am certainlyandabsolutely in every way comfortable with what I have reported".
Mr Bannon had helped Mr Trump form a coalition of anti-establishment Republicans, blue-collar working class and economic nationalists that launched him to the White House, but Mr Trump had long ago grown frustrated that Mr Bannon seemed to be overstepping his role.
"What's the president's reaction to the growing number of suggestions, both in this book and in the media, that he's mentally unfit to serve as president?"
The US President wrote: "Michael Wolff is a total loser who made up stories in order to sell this really boringanduntruthful book".
That suit, brought by Summer Zervos, a former contestant on "The Apprentice", could force Trump to address sexual harassment claims against him.
Some reporters did look at Wolff's past andfound reason to doubt his latest account.
Michael Wolff's book, "Fire and Fury: Inside the Trump White House", was released Friday. Wolff characterizes Trump as uninformed and at times erratic since he became president.
White House press secretary Sarah Saunders said the book is "filled with false and misleading accounts" and is "trashy tabloid fiction". "Now it was within 10 minutes", the book says. According to the book, Trump uses Just For Men hair color, but he doesn't have the patience to wait for the dye to set. "The man does not read, does notlisten".
Certainly he was very open with me, accessible with me, and then he started to talk. One popular bookstore, KramerBooks, began selling "Fire and Fury" at midnight Friday.
Even those werenot the extent of Bannon's remarks, however.
"The big picture here is of a White House that is chaotic, of a president whose impulses whipsaw the White House of a lot of backstabbing, front-stabbing", said John Dickerson, host of the CBSNews program "Face the Nation".