Woodward's book comes less than a month after former White House aide Omarosa Manigault-Newman published a tell-all account of her first year in the Trump administration, calling the president a "con" and a "racist".
"It's just nasty stuff", Trump said.
In the same statement issued Tuesday afternoon, White House chief of staff John Kelly called Woodward's contention "not true" that he once referred to the president as an "idiot", describing his relationship with his boss as "incredibly candid and strong".
President TrumpDonald John TrumpBrennan defends Kaepernick: He didn't kneel "to disrespect our flag" Trump warns Syria against attack on rebel stronghold: "Don't let that happen" Omarosa celebrates second week on bestsellers list despite "hit-pieces" from Trump allies MORE in a tweet Tuesday night denied allegations in reporter Bob Woodward's forthcoming book that he called Attorney General Jeff SessionsJefferson (Jeff) Beauregard SessionsFlake rips Trump's attack on Sessions: He's trying to use DOJ to "settle political scores Fox News" Brit Hume to Trump: Sessions's job "is not to play goalie for a president" Republican senator slams Trump's DOJ attack: USA "not some banana republic" MORE "mentally retarded" and a "dumb Southerner".
Mr Mattis told Mr Trump he would "get right on it", but instead developed a plan for a limited air strike that did not threaten Mr Assad personally.
Woodward's book includes the claim that Mattis said Trump's understanding of North Korea was that of a "fifth or sixth grader".
White House Spokeswoman Sarah Sanders said the book was "nothing more than fabricated stories, many by former disgruntled employees, told to make the president look bad".
"I think the President of the United States can not be seen taking the fifth". After all, his investigations with Washington Post colleague Carl Bernstein helped bring down Richard Nixon and he has written books on many leaders, including George W Bush and Barack Obama.
Another allegation made in the book is that former top economic adviser to Trump Gary Cohn stole a letter off Trump's desk to prevent the U.S. from withdrawing from a trade agreement with South Korea.
Woodward quotes an exasperated Chief of Staff John Kelly doubting Trump's mental faculties, declaring during one meeting, "We're in Crazytown".
"I'll just take the paper off his desk", Mr Cohn told another White House aide, according to the book. The national security team developed options for the more conventional airstrike that Trump ultimately ordered.
"He just made something up".
Mr Woodward writes that Mr Trump was presiding over "a nervous breakdown of the executive power of the most powerful country in the world". I do not even know why any of us are here.
Supposedly, Trump also called Sessions "mentally retarded".
Mattis says in the statement: "While I generally enjoy reading fiction, this is a uniquely Washington brand of literature, and his anonymous sources do not lend credibility".
"The contemptuous words about the President attributed to me in Woodward's book were never uttered by me or in my presence".
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 says.
Trump says he "probably would have preferred to speak to (Woodward), but maybe not". This is the worst job I've ever had, ' he supposedly said during one meeting.