Woodward used as an example Trump's complaint about USA troops still on the Korean peninsula, leaving Defense Secretary James Mattis to explain "we're doing this to prevent World War III".
The people who work for Trump worry that Trump will give orders that threaten the security of the country or the world, Woodward said.
Woodward asserted on CBS Sunday Morning that "people who work for him are anxious - that he will sign things or give orders that threaten the national security or financial security of the country or the world".
"Time and time again people will deny things", Woodward says.
"I have really no idea, nor do you, what else this person has divulged", Conway told Tapper.
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"The incidents are not anonymous", Woodward said. In the book, which has been previewed by The Washington Post, Kelly is said to have called the president an "idiot", while Mattis reportedly compared Trump's intellect to that of a "fifth or sixth grader".
The decision not to include the weapons in the parade is seen as a move to placate Donald Trump and continue decreasing the tension between the nations that had existed before, an analyst told the New York Times. He said he had talked to more than 100 people, and that half of them are key sources for the book.
Woodward's book is a tragicomic catalogue of life in a White House lorded over by an apparently unmoored president, even as top officials such as former economic adviser Gary Cohn snatched potentially destructive documents off the president's desk so he wouldn't sign them.
That said, consider what we are talking about here: One of the two reporters primarily responsible for a series of stories detailing corruption at the highest level of the Nixon government and a man who has spent the last four decades reporting and chronicling how each successive president since Nixon has dealt with the huge challenges of the office, is now suggesting that what he saw in the Trump White House is unlike what he's seen before.
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Woodward's book - "Fear: Trump in the White House" - is to be released next week.
In a statement to The Washington Post, Woodward said, "I stand by my reporting". "I wouldn't be surprised if it was one of [Woodward's] sources and he encouraged him to go public with it".
Trump on Monday morning tweeted "We are making some of the biggest and most important deals in our country's history - with many more to come!"
Later on during the interview, Woodward put Guthrie on the spot, when she questioned him about specific portions of his book. The president has yet to say whether he'd go that far, but Pence says he'd be willing to submit to such an examination. He pointed to another instance described in the book, a meeting of the National Security Council in which Trump questions why the U.S.is funding military defenses in Europe. "It's very important whether this is somebody who witnessed and participated", Woodward said.
The Vice President also argued that the author of the Times article was guilty of more than just disloyalty.
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White House press secretary Sarah Sanders says the Department of Justice should look into any attempt to undermine the executive branch, says it's "sad and pathetic" that the anonymous author of the New York Times op-ed is receiving so much media attention.