He praised Trump's legislative accomplishments, which he said Woodward's book ignores, and said the president "invites robust discussion" from aides.
Trump told journalists he "really" appreciated the pair's statements, which helped show that "the book is just a piece of fiction".
The White House has spent more than a week battling the allegations in Mr.
Several people in Trump's orbit have called the book's accuracy into question, while Woodward has maintained several times that he stands by his reporting.
"That's fine", Cohn said, Woodward reports.
Woodward's said he won't name the official but was happy with his public statement.
The White House under President Donald Trump is mired in a perpetual "nervous breakdown" with staff constantly seeking to control a leader whose anger and paranoia can paralyze operations for days, according to a new book by Bob Woodward. This, during a conversation on Afghanistan, during which Trump also said, according to Woodward, that Modi told him the United States had "gotten nothing out of Afghanistan". Woodward attributed to him were "incorrect" and that he hadn't been called by Mr. Trump said in his tweet.
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Woodward went on to say, "People who work for him are anxious. that he will sign things or give orders that threaten the national security or the financial security of the country, or of the world".
The president also floated an idea for making money from the recent rise in interest rates, according to Woodward.
Gary Cohn, who was the chief White House economic advisor, went so far previous year as to steal an order from Trump's desk that, if the president had signed it, would have cancelled the US-South Korea trade agreement.
Woodward explains: McMaster, he says, "understood the strategic importance of India, a sworn enemy of Pakistan".
Moreover, Press Secretary Sarah Huckabee Sanders, Chief of Staff John Kelly, Secretary of Defense James Mattis, and other top officials have all slammed Woodward for his allegedly untrue claims.
The White House and some officials named in the book have attacked Woodward, taking aim at his credibility. "People closest to him do not trust him", he added, "And the impulse-driven presidency is something that the more people know, the more they realize we're at risk".
"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".