Mr Woodward released Fear: Trump in the White House – an explosive book which paints a portrait of a White House in chaos – on Tuesday.
Mr Woodward, an associate editor at The Washington Post, spoke to dozens of current and former officials for background but their names were not used. The book depicts a West Wing where aides disparage Mr Trump and strive to stop him from making calamitous choices.
The book, which has been No 1 on Amazon since details first started surfacing a week ago, includes a conversation between Mr Trump and a “friend who had acknowledged some bad behaviour towards women”.
While the friend was not named, the president provided him with some advice.
According to the book, Mr Trump – who has been accused by more than a dozen women of inappropriate sexual behaviour – told the friend it is a mistake to display weakness in the face of such accusations.
“You’ve got to deny, deny, deny and push back on these women,” Mr Trump said, according to Mr Woodward. “If you admit to anything and any culpability, then you’re dead. That was a big mistake you made.”
Mr Trump said it was critical to show no hesitation in denying accusations and go on the attack and push back instead.
“You didn’t come out guns blazing and just challenge them. You showed weakness,” he reportedly told the friend. “You’ve got to be strong. You’ve got to be aggressive. You’ve got to push back hard. You’ve got to deny anything that’s said about you. Never admit.”
It is not clear when the comments were alleged to have been made.
At least 19 women have publicly accused Mr Trump of kissing them, touching them inappropriately or having an affair with him while he was married.
The billionaire property developer, who has denied all the accusations, is also currently in the process of fighting multiple lawsuits, including one by former Apprentice contestant Summer Zervos.
Ms Zervos claims Mr Trump sexually assaulted her in 2007 and filed a lawsuit in New York after Mr Trump accused her of lying.
A judge recently ruled Mr Trump would have to answer questions under oath in regards to the defamation lawsuit Ms Zervos brought against him.
Mr Trump has dismissed Mr Woodward’s book as a “joke”, tweeting on Monday: “The Woodward book is a Joke – just another assault against me, in a barrage of assaults, using now disproven unnamed and anonymous sources. Many have already come forward to say the quotes by them, like the book, are fiction. Dems can’t stand losing. I’ll write the real book!”
The Woodward book is a Joke – just another assault against me, in a barrage of assaults, using now disproven unnamed and anonymous sources. Many have already come forward to say the quotes by them, like the book, are fiction. Dems can’t stand losing. I’ll write the real book!
— Donald J. Trump (@realDonaldTrump) September 10, 2018
Several former aides of Mr Trump have sought to distance themselves from the book’s portrayal of the West Wing.
Former White House staff secretary Rob Porter and Gary Cohn – who was previously the chief economic advisor to Mr Trump – both pushed back against the book.
While neither former staffer directly denied details in the book, Mr Porter issued a statement to say the book offers a “selective and often misleading portrait.” Mr Cohn told Axios the “book does not accurately portray my experience at the White House.”
Mr Woodward has steadfastly defended his work in an extensive media tour. On Tuesday, Amazon said Fear: Trump in the White House was out of stock and would be available to ship in one to three weeks.