According to CNBC, White House Press Secretary Sarah Huckabee Sanders said in a statement, "This book is nothing more than fabricated stories, many by former disgruntled employees, told to make the president look bad".
According to the book, Mr Trump told Defense Secretary Jim Mattis that he wanted to have Mr Assad assassinated after the Syrian president launched a chemical attack on civilians in April 2017.
Chief of Staff Kelly repeatedly calls Mr Trump an "idiot" and said that "it's pointless to try to convince him of anything".
The President allegedly shouted: "Let's ******* kill him!"
"I've been on the receiving end of a Bob Woodward book", he tweeted Tuesday.
Readers shouldn't expect too many pages focusing on Trump's family, but the book does include at least one feisty exchange between Ivanka Trump and Steve Bannon, the former chief White House strategist.
Woodward's book is based on hundreds of hours of taped interviews and dozens of sources in Trump's inner circle, along with documents, memos and diaries, CNN said.
Bob Woodward, who gained national fame for his reporting on the Watergate scandal in the 1970s, talked to top aides for the book with the understanding that he would not reveal how he got his information, the Post said. "He's gone off the rails", Kelly was quoted in the book as saying.
"It's either that or an orange jumpsuit". He's this dumb Southerner. Dowd, who has since resigned, believed the president had nothing to hide but was incapable of giving simple factual answers. But the book is filled with derogatory descriptions about the president by senior advisors.
Dowd wrote "no" when asked if he ever described Trump as a "fucking liar", warned Trump he risked an "orange jump suit", or described Trump's interview prep to Mueller, as quoted by CNN. So one thing is certain: We're going to be hearing a lot more about this for the rest of September.
Mr Mattis told associates after a separate incident that Mr Trump acted like "a fifth or sixth-grader (primary school student)", according to the book.
"It's really too bad, because nobody told me about it, and I would've loved to have spoken to you".
Trump reportedly attacked his attorney general, Jeff Sessions, in private even more harshly than he does in his regular Twitter tirades about the first U.S. senator to endorse his presidential campaign. Meanwhile, Kelly has issued a statement denying that he "ever called the President an idiot". One reason McMaster dresses as he does is that he has spent his life serving his country, rather than making money.
Kelly is depicted by Woodward as decrying the climate in the White House as "Crazytown" and blasting the president as "an idiot". I think it probably wouldn't have made a difference in the book.
The President is also said to have lashed out at former NY mayor Rudy Giuliani, now his attorney, and reportedly said he was a "baby" after he appeared on TV to defend Mr Trump over harassment allegations.
Months later, Woodward recounted that Trump told Dowd, "I'll be a real good witness".