According to the book, Mr Cohn "stole a letter off Trump's desk" that the President was intending to sign to formally withdraw the USA from a trade agreement with South Korea.
The book also describes a conversation in which Trump told Defence Secretary James Mattis to assassinate Syrian leader Bashar al-Assad after the Syrian government launched a chemical attack on civilians in April 2017. Mr Mattis explained troops were there "in order to prevent World War III".
Later Mattis told associates Trump had the national security understanding of a "fifth or sixth grader".
Not only that, the book further mentions that Defence Secretary James Mattis likened his intellect to "a fifth or sixth grader" - a child aged 11 or 12 and Trump's lawyer John Dowd is said to have deemed him a "f****** liar" and warned of jail if he agreed to a formal quiz over Russian Federation links.
The White House press secretary, Sarah Sanders, dismissed the book as "nothing more than fabricated stories, many by former disgruntled employees".
"In serving in this administration, the idea that I would show contempt for the elected Commander-in-Chief, President Trump, or tolerate disrespect to the office of the President from within our Department of Defense, is a product of someone's rich imagination".
The Washington Post reports that Conway has privately been telling people that "Woodward was credible and that his book could be damaging".
The book says the US President's former economic adviser, Gary Cohn, removed a letter about a trade agreement with South Korea because he thought it was a threat to national security. "We're in Crazytown", Kelly said, according to Woodward.
The 448-page book, "Fear: Trump in the White House", is slated for public release on September 11.
Mr Trump later authorised a conventional air strike on Syria.
"He just made something up". The administration also released the terms of a renegotiated Korus on Monday that makes what most trade experts consider to be only minor tweaks.
Trump suggested that one of the lone ways Woodward may have been able to reach him was to get in touch with his scheduler, 27-year-old Madeleine Westerhout. Trump asks in the call. I do not even know why any of us are here.
U.S. President Donald Trump took to Twitter Tuesday night to deny that he called Attorney General Jeff Sessions "mentally retarded" and a "dumb southerner". "While I generally enjoy reading fiction, this is a uniquely Washington brand of literature, and his anonymous sources do not lend credibility", Mattis said in a statement. "He made this up to divide!", Mr Trump said in the Tweet.
The president's attorney also anxious that if a transcript of the interview leaked, as it inevitably would, people would say, "I told you he was an idiot".
"Despite Trump's reported insistence that he would be "a real good witness" in an interview with Special Counsel Robert Mueller, the president's former lawyer John Dowd-who resigned in March-firmly believed that Trump would commit perjury if he talked to Mueller".
Woodward claims that Trump once asked Mattis why the US backs South Korea militarily and financially, prompting the defense secretary to tell close associates afterward that Trump had the understanding of a fifth or sixth grader. "Secretaries of defense don't always get to choose the president they work for", Mattis allegedly said in another instance.
The are quoted as calling him an "idiot" and a "liar".
Trump says he "probably would have preferred to speak to (Woodward), but maybe not". "So I have another bad book coming out. It's either that or an orange jumpsuit".