announced their departure from Trump's business advisory councils following the controversial comments.
Said Woodward, "Some of the things that Trump did and does jeopardizes the real national security".
"Most significant, however, were the private reactions from House Speaker Ryan and Senate Majority Leader McConnell".
"They're not telling the truth", Woodward said.
The book, "Fear: Trump in the White House", is scheduled for release on Tuesday.
Trump even (mis) quoted Today host Savannah Guthrie asking guest Woodward about the book, though in Trump's tweet her question is meant to sound more like a condemnation.
Monday morning, Trump took to Twitter to slam the book.
Ms. Gurthrie pressed on the statements his book attributes to Chief of Staff John Kelly and Secretary of Defense James Mattis, which both have denied.
White House press secretary Sarah Sanders said on Monday that the anonymous author of the New York Times op-ed that is searingly critical of Donald Trump's ability to be president, is "attempting to undermine the executive branch", and added that the US Department of Justice should "look into" the writer's identity.
"A number of people have come out and said Woodward never even reached out to corroborate, which seems incredibly reckless for a book to make such outrageous claims, to not even get a $10 fact checker", Sanders said.
Sanders replied that if an individual is trying to undermine the presidency and is potentially attending meetings where national security is being discussed, "that would certainly be problematic and something the Department of Justice should look into". "Family members of the 28,000 people there.'" Trump never sent the tweet, because the US got a back-channel message from North Korea saying Kim would see such a pullout as proof the USA was about to attack, Woodward explained.
Asked later whether the White House would list all the things in Woodward's book that are wrong, Sanders said such an exercise "would be a complete and utter waste of our time, so no".
Trump tweeted that "the Woodward book is a Joke - just another assault against me, in a barrage of assaults, using now disproven unnamed and anonymous sources". "If that person had come to me while I was working on this book or if it were someone I interviewed I would say, 'I need specifics.' The building blocks of journalism, of truth, are specific incidents".
"These are political statements to protect their jobs - totally understandable", Woodward said. Democrats can't stand losing. He said his book "is as carefully done as you can do an excavation of the reality of what goes on". "I'll write the real book!" "I hope [Trump] knows - maybe he does? - that there are dozens and dozens of us".