Sulzberger said the newspaper believed the piece crossed the threshold for using an anonymous source.
The anonymous author said that similar-minded officials within the administration are "trying to do what's right even when Donald Trump won't".
In another, Woodward recounts how White House Chief of Staff John Kelly frequently became angry and told colleagues that he thought the President was "unhinged".
"Let's talk about your process a little bit because we live in an era where the president talks about fake news".
Trump called it a "work of fiction" last week and sought to discredit Woodward's reputation. "You know, people get complacent. You have millions and millions of Americans who voted for this".
He praised Trump's legislative accomplishments, which he said Woodward's book ignores, and said the president "invites robust discussion" from aides. "The soldiers had told him that North Atlantic Treaty Organisation staff were totally dysfunctional", says the book. He's gone off the rails.
"I'm not because I know what I did and I'm not anxious about it", he said, again denying that he spoke to his father about his June 2016 Trump Tower sit-down with a Russian lawyer promising dirt on Hillary Clinton. "It's the worst job in America". In one part, Woodward writes: 'Mattis was particularly exasperated and alarmed, telling close associates that the president acted like - and had the understanding of - "a fifth- or sixth-grader"'.
"Are they lying?" Guthrie asked Woodward. What I want to focus on is - here's the problem.
International Criminal Court threatened with U.S. sanctions
But in practice, according to Bolton, the court's biggest supporters have used it as a tool to constrain the United States. Mr Bolton said neither Afghanistan nor any government signatory to the ICC's statute had requested an investigation.
Equally seriously, Woodward claims that after Trump was put through a rehearsal for testifying before special counsel Robert Muller, his then-lawyer advised, "Don't testify". The defence secretary also faced down an order from Trump to assassinate Bashar al-Assad after the USA president learned that Assad had used chemical weapons in Syria's civil war.
In spite of denials, Woodward's book has traction because of his meticulous methods.
"Does this ring true?"
The journalist then says how Dowd told Trump that he either do it his way or get "fitted for an orange jumpsuit".
"And I sometimes did just that", Porter said. "Does it ring true?"
The source, while citing demeaning views of Trump from other unnamed senior officials, declined to say how many officials had actually taken this vow of resistance, or when and how they had taken this vow. Dems can't stand losing.
"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. "Trump wasn't buying it", writes Woodward.
Though the media has breathlessly praised Woodward's new book, there are credibility issues with the journalist at hand.