"My credibility is being questioned by a man who has less credibility than, perhaps, anyone who has ever walked on earth at this point", Wolff said on NBC's "Today" show on Friday.
"I work like every journalist works".
"I have to learn how he takes information in, processes it and makes decisions", Tillerson told CNN. "I am certainly and absolutely, in every way, comfortable with everything I've reported in this book".
While Wolff stands by his reporting, Trump and his associates are not the only ones questioning the author's veracity.
Sanders said that Bannon met on "multiple occasions" with Michael Wolff, author of "Fire and Fury: Inside the Trump White House". "I can see several places in the book that are wrong. But it certainly was not off the record".
Wolff says the book is mostly based on talks with people who have worked closely with the president. She is a billionaire GOP donor and co-owner of Breitbart, the populist website that Bannon helps run.
Mr Tillerson dismissed suggestions that his stint as top US diplomat is coming to an end, amid reports of a rocky relationship with Mr Trump. Her defamation suit against Trump claims that the president damaged her reputation when he subsequently called her a liar. "Does not listen. He's like a pinball, just shooting off the sides".
Wolff said the book, which portrays Trump as a "child" and the White House as chaotic, is drawn from his regular access to the West Wing and more than 200 interviews, including some three hours with Trump himself. The letter also insists that a "full and complete retraction" be issued, along with an apology to Mr. Trump.
Wolff's critics aren't limited to 1600 Pennsylvania Avenue. In one story, Trump was at his Mar-a-Lago resort in Florida over the winter holiday break, and failed to recognise old friends.
Trump's lawyers had tried to block publication of the book, however, the book has now gone on sale.
On Friday afternoon, no copies were available at Barnes & Noble locations at the Concord and Christiana malls.
For this reason, he said the White House is "sitting on a beach trying to stop a Category Five" hurricane.
"He seemed almost phobic about having formal demands on his attention", Wolff wrote.
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