And he denied accounts in the book that senior aides snatched sensitive documents off his desk to keep him from making impulsive decisions. He said in an interview with the Daily Caller: "There was nobody taking anything from me."
The publication of Woodward's book has been anticipated for weeks, and current and former White House officials estimate that nearly all their colleagues cooperated with the famed Watergate journalist.
The White House, in a statement from press secretary Sarah Huckabee Sanders, dismissed the book as "nothing more than fabricated stories, many by former disgruntled employees, told to make the President look bad."
Woodward did not immediately respond to a request for comment.
The book quotes chief of staff John Kelly as having doubts about Trump's mental faculties, declaring during one meeting, "We're in Crazytown." It also says he called Trump an "idiot," an account that Kelly denied.
The book says Trump's former lawyer in the Russia probe, John Dowd, doubted the President's ability to avoid perjuring himself should he be interviewed in Special Counsel Robert Mueller's investigation into Russian election interference and potential coordination with Trump's campaign. Dowd, who stepped down in January, resigned after the mock interview, the book said.
"Don't testify. It's either that or an orange jumpsuit," Dowd is quoted telling the President.
Dowd, in a statement, said "no so-called 'practice session' or 're-enactment'" took place and denied saying Trump was likely to end up in an orange jumpsuit.
Defence Secretary Jim Mattis is quoted explaining to Trump why the US maintains troops on the Korean Peninsula to monitor North Korea's missile activities. "We're doing this in order to prevent World War III," Mattis said, according to the book.
The book recounts that Mattis told "close associates that the president acted like — and had the understanding of — 'a fifth- or sixth-grader.'"
Mattis said in a statement: "The contemptuous words about the President attributed to me in Woodward's book were never uttered by me or in my presence."
Woodward reported that after Syria's Bashar al-Assad launched a chemical weapons attack on civilians in April 2017, Trump called Mattis and said he wanted the Syrian leader taken out, saying, "Kill him! Let's go in."
Mattis assured Trump he would get right on it but then told a senior aide they'd do nothing of the kind, Woodward wrote. National security advisers instead developed options for the airstrike that Trump ultimately ordered.
US Ambassador Nikki Haley denied that Trump had ever planned to assassinate Assad. She told reporters at UN headquarters that she had been privy to conversations about the Syrian chemical weapons attacks, "and I have not once ever heard the President talk about assassinating Assad."
She said people should take what is written in books about the President with "a grain of salt."
Woodward also claims that Gary Cohn, the former director of the National Economic Council, boasted of removing papers from the President's desk to prevent Trump from signing them into law, including efforts to withdraw from the North American Free Trade Agreement and from a deal with South Korea.
The book quotes Trump as mocking his Attorney-General, Jeff Sessions, who has been a target of the President's wrath since recusing himself from the Russia investigation.
"This guy is mentally retarded," Trump said of Sessions, according to the book. "He couldn't even be a one-person country lawyer down in Alabama."
Trump did not speak to Woodward until after the book's manuscript was completed. The Post released audio of Trump expressing surprise about the book in an August conversation with Woodward and dismay that he did not have an opportunity to contribute. Woodward tells Trump he had contacted multiple officials to attempt to interview Trump and was rebuffed.
"I never spoke to him," Trump told the Daily Caller. "Maybe I wasn't given messages that he called. I probably would have spoken to him if he'd called, if he'd gotten through."
The book follows the January release of author Michael Wolff's "Fire and Fury," which led to a rift between Trump and Steve Bannon, his former chief strategist, who spoke with Wolff in terms that were highly critical of the president and his family. Wolff's book attracted attention with its vivid anecdotes but suffered from numerous factual inaccuracies.
Woodward's work also comes weeks after former White House aide and Apprentice contestant Omarosa Manigault Newman published an expose on her time in the West Wing, including audio recordings of her firing by Kelly and a follow-up conversation with the President in which he claimed to have been unaware of Kelly's decision.
While White House aides have become increasingly numb to fresh scandals, the book still increased tensions in the West Wing, especially given the intimate details shared and the number of people Woodward appeared to have interviewed. Some White House officials expressed surprise at the number of erstwhile Trump loyalists willing to offer embarrassing stories of the president and his inner circle.
White House aides coordinated with other officials quoted in the book to dispute troublesome passages. But insiders speculated the fallout could be worse than that from Fire and Fury, given Woodward's reputation.
Woodward's account relies on deep background conversations with sources, meaning their identities are not disclosed.
Former George W. Bush press secretary Ari Fleischer defended Woodward's methodology. "I've been on the receiving end of a Bob Woodward book," he tweeted. "There were quotes in it I didn't like. But never once - never - did I think Woodward made it up."
He adds: "Anonymous sources have looser lips and may take liberties. But Woodward always plays is straight. Someone told it to him."
- AP