In the interview, Woodward discussed his new book "Fear: Trump in the White House", and said Trump is fixated on the fact that the USA spends $US3.5 billion a year to station troops in South Korea in order to maintain military presence on the peninsula.
The President took immediate steps to address the situation on Monday, hitting out at Bob Woodward's new book, which, along with an op-ed by an anonymous senior official in the New York Times, presents a devastating picture of his performance.
"He tells an associate, 'I have to protect the country because this will unravel a trade deal which will jeopardize one of the most important intelligence operations we have going on, '" Woodward said, adding the documents are printed in the book.
Woodward resisted Guthrie's attempts to verify his sourcing for his book about Trump, warning Americans that the president was putting the country in grave danger.
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Woodward said of the president, "There's a war on truth by him".
The book also quotes Mattis, after a contentious National Security Council meeting on January 19, as saying Trump acted like and had the understanding of "a fifth or sixth-grader".
Woodward told Guthrie today that the sources he quotes who are denying their words are now "not telling the truth". In the book, several senior administration officials, including Chief of Staff John Kelly and Defense Secretary Jim Mattis, are described making disparaging remarks about Trump.
"You crank out the great Washington denial machine", he says.
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"Mattis says to him, 'We're doing this to prevent World War III", Woodward said. But I've done hundreds of hours of interviews with people.
"I would agree to take it in a heartbeat and submit to any review the administration wanted to do", Pence said.
Actually, Guthrie's question was a softball, giving Woodward a chance to explain, somewhat confusingly, that his sources might be anonymous but the "incidents" are not.
Woodward goes on to say that he's "never seen an instance when the president is so detached from the reality of what's going on".
"You can, in an nearly microscopic way, establish what occurred - and that's what I've done in this book".
The President also lashed out on Wednesday and dismissed the op-ed as "really a disgrace" and "gutless" and assailed the author and the Times for publishing the anonymous opinion piece.
"Again and again, Woodward recounts at length how Trump's national security team was shaken by his lack of curiosity and knowledge about world affairs and his contempt for the mainstream perspectives of military and intelligence leaders", The Post said.
"Without knowing who it was, it's very hard to know how much weight you should put on it", he said.
The text of the op-ed was pulled apart for clues: The writer is identified as an "administration official"; does that mean a person who works outside the White House?