Woodward says: "I believe in our country, and because you're our president, I wish you good luck".
Regarding the fraught relationship between the president and his chief of staff, the Post reported Woodward found that Kelly "frequently lost his temper" over Trump, and that he thought the president was "unhinged".
A central theme of the book is the stealthy machinations used by those in Trump's inner sanctum to try to control his impulses and prevent disasters, both for the president personally and for the nation he was elected to lead.
Excerpts were released Tuesday and the full book is set for release September 11.
"Certainly the president is his own best story teller and his own best advocate for his policies", Sanders said.
The publication of Woodward's book has been anticipated for weeks, and current and former White House officials estimate that almost all their colleagues cooperated with the famed Watergate journalist. 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.
A Pentagon spokesman, Col. Rob Manning, said Mattis was never interviewed by Woodward.
"Let's go in. Let's kill the f--ing lot of them", Trump said, the book alleges.
In another reported excerpt, Woodward writes that Trump told Defense Secretary Jim Mattis that he wanted to assassinate Syrian leader Bashar Assad after a chemical attack in April 2017.
Speaking to reporters at the White House, Sanders said the book did not accurately depict the administration, adding that it had been "pretty widely pushed back on". She told reporters at United Nations 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".
"The things I see coming out of this White House are the president delivering on historic tax cuts, delivering on building a booming economy, delivering on rebuilding our military, delivering on remaking the judiciary, delivering on cutting regulation after regulation. We're going to be much more measured".
The president's tweet was part an aggressive effort by the White House to discredit Woodward's forthcoming book, "Fear", which paints a harrowing portrait of the Trump presidency, based on in-depth interviews with administration officials and others.
"The idea I ever called the President an idiot is not true", Kelly said, adding that the claim "is another pathetic attempt to smear people close to President Trump and distract from the administration's many successes".
Stephanopoulos also asked Sarah about the president's tweet over the weekend that called attention to the investigations of two "popular" Republican congressmen facing serious corruption charges.