Mr Trump's former lawyer, John Dowd, conducted a mock interview with Mr Trump to convince him that he would commit perjury if he agreed to talk to Special Counsel Robert Mueller, who is leading the Russian Federation investigation, the book claims.
Dowd then explained to Mueller and Quarles why he was trying to keep the president from testifying: "I'm not going to sit there and let him look like an idiot". He has gone off the rails.
Former top economic adviser Gary Cohn so feared that the programme would be at risk if Trump signed a letter formally withdrawing the United States from a South Korean trade agreement that he stole the letter from the Oval Office desk, said CNN, which also obtained a copy of Woodward's book.
Trump reportedly attacked his attorney general, Jeff Sessions, in private even more harshly than he does in his regular Twitter tirades about the first U.S. senator to endorse his presidential campaign.
The White House also released a statement attributed to Kelly in which he renewed his denial of ever calling Trump an "idiot".
The chemical attack, which was carried out by Assad, killed dozens and prompted a US missile strike against a Syrian air base which Washington said was used to launch the strike. "Let's f-ing kill him!"
President Trump's top aides were so anxious about his plans to scrap two major trade deals that they swiped the orders off his desk - and he didn't even notice, according to a new book on the White House.
The Watergate reporter wrote that Mattis once described President Trump as having the understanding of "a fifth- or sixth-grader" when it comes to the Korean Peninsula, according to The Washington Post.
Mr Trump tells Commerce Secretary Wilbur Ross he does not trust him, saying: "I don't want you doing any more negotiations". "Mr. President, I'm afraid I just can't help you".
Woodward's negotiations for an interview with Trump fell through, although the president tried belatedly to talk to the journalist after the manuscript had been completed.
Trump reportedly mocked the accent of his Attorney General, Jeff Sessions: "This guy is mentally retarded. He's this dumb Southerner", he said of the former GOP senator.
In a statement, Dowd said that he had not read Woodward's book and pushed back against Woodward's reporting, including the "orange jumpsuit" comment, the practice session and the re-enactment.
Add Trump's former lawyer John Dowd to the long list of White House insiders who apparently do not have very much confidence in the president.
A President who prizes loyalty and self-image above all is left exposed and isolated in his own White House, viewed with contempt by those who serve him and open to ridicule by others who see his swaggering, domineering brand as a front for inadequacy.
Perhaps some of the strongest rhetoric came from former FBI Director James Comey, who called Trump "morally unfit to be president", "untethered to truth", and "unethical".
White House press secretary Sarah Sanders called the book "nothing more than fabricated stories, many by former disgruntled employees".
The publication of Woodward's book has been anticipated for weeks, and current and former White House officials estimate that almost all of their colleagues cooperated with the noted journalist.
While White House aides have become increasingly numb to fresh scandals, the latest book still increased tensions in the West Wing, especially given the intimate details shared and the number of people Woodward appeared to have interviewed.
"He's had a lot of credibility problems", Trump said of Woodward.