"I like him very much", Trump is quoted as saying by Woodward.
"The idea that the Secretary of Defense has to tell the president that all of these actions are created to prevent the ultimate catastrophe", Woodward said.
Earlier, Trump said he would pen his own book with the real story of his accomplishments.
Woodward - whose reporting with then-Washington Post colleague Carl Bernstein helped take down President Richard Nixon, and who has penned several deep-dive nonfiction books on presidents since - explores the paranoia that he says drives Trump's White House.
Donald Trump has the IQ of an "inbred tanning bed", according to the president's former chief economic advisor, Gary Cohn.
"A third of my job was trying to react to some of the really risky ideas that he had and try to give him reasons to believe that maybe they weren't such good ideas", Porter told an associate, according to the book.
"To my knowledge, that is correct", he said. Although Trump has defended Mattis against Woodward's insinuations, the pressure to replace Mattis with another more hawkish defense secretary is still ongoing.
Trump has blasted the book ahead of its release, calling its author a "liar" on Twitter. Whereas at first Woodward claims that this order, which Trump had not seen, had come from "unknown channels", subsequently he revises himself: "At least twice, Porter had the order drafted as the president had directed".
The highly anticipated book, which chronicles some unflattering moments in the Trump administration, has been sourced from numerous current and former officials.
A similar situation also occurred involving a letter about trade with South Korea, he said.
Reader interest in the inner workings of the Trump White House is showing no signs of fading. Incredibly, Woodward cites Trump's statement on Tillerson's firing while editing out the Iran reference.
Trade talks between Foreign Affairs Minister Chrystia Freeland and her US counterpart Robert Lighthizer resumed this week in Washington, just as Prime Minister Justin Trudeau warned of a "massive disruption" and job losses on both sides of the border if Trump follows through on his threat to impose auto tariffs.
Woodward's book is now available through third-party sellers on Amazon but displays a shipping estimate of "one to three weeks", implying a serious shortage of copies.
"We should just go borrow a lot of money right now, hold it, and then sell it to make money", Trump suggested.
He said the book was "the product of someone's rich imagination".
Trump also derided his predecessor's return to politics.
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