"Let's go in. Let's kill the f---king lot of them," Trump said in one of the highlights of the 448-page book that was described in an article Tuesday in The Washington Post, where Woodward has long worked. "Fear" is slated for a Sept. 11 release.
Woodward says in the book that he conducted hundreds of hours of interviews with participants and witnesses in the conversations he writes about. He also had taped notes, diaries and government documents.
The interviews were granted on the condition of "deep background," which according to Woodward meant that while he could write what happened, he could not reveal the sources of particular stories.
The Washington Post, in a separate article Tuesday, published a lengthy transcript of a call last month between Trump and Woodward, during which the president said, "I would've loved to have spoken to you" for the book.
Woodward replied that he had sought an interview with the president through about a half-dozen people, including senior presidential advisor Kellyanne Conway and White House spokesman Raj Shah.
"They don't tell me," Trump said.
Mattis is depicted in the book as being "particularly exasperated and alarmed" by having to tell Trump that "we're doing this in order to prevent World War III" to justify the presence of the U.S. military on the Korean Peninsula.
Mattis told associates that Trump "acted like — and had the understanding of — 'a fifth- or sixth-grader,' " according to the book.
But Trump is quoted in "Fear" as being scornful of the intelligence of Sessions, a former Alabama senator whom he has long blamed for recusing himself in the Russian investigation, a step that led to Mueller's appointment.
"He's this dumb Southerner. … He couldn't even be a one-person country lawyer down in Alabama," Trump reportedly said of Sessions.
A Justice Department spokesman declined to comment to CNBC when asked about the president's characterization of Sessions, who heads the department.
Woodward also writes that Trump exploded in a rage after a practice interview with his own lawyer John Dowd playing the role of Mueller, as they prepared for a potential sit-down with the special counsel.
"This thing's a goddamn hoax," Trump fumed, according to the book. "I don't really want to testify."
Dowd was sure that Trump would committ perjury if he did talk to Mueller, Woodward wrote.
But when Dowd told Trump, "Don't testify," warning that "It's either that or an orange jumpsuit," the president pushed back.
"I'll be a real good witness," Trump reportedly said.
"You are not a good witness," Dowd retorted, according to the book.
The attorney quit the day after their conversation.
White House Press Secretary Sarah Huckabee Sanders, in a prepared statement, said, "This book is nothing more than fabricated stories, many by former disgruntled employees, told to make the President look bad."
According to the Post's account of the book, Kelly despaired of dealing with Trump, whom he called "unhinged" during discussions with colleagues in the White House.
"He's an idiot. It's pointless to try to convince him of anything. He's gone off the rails," Kelly was quoted in the book as saying.
He added, "We're in Crazytown. I don't even know why any of us are here. This is the worst job I've ever had."
Kelly on Tuesday said, in a prepared statement: "The idea I ever called the President an idiot is not true."
"As I stated back in May and still firmly stand behind: 'I spend more time with the President than anyone else, and we have an incredibly candid and strong relationship. He always knows where I stand, and he and I both know this story is total BS. I'm committed to the President, his agenda, and our country. This is another pathetic attempt to smear people close to President Trump and distract from the administration's many successes.' "
Kelly's statement referred to an earlier one he had made in May, after NBC News first reported that he had called Trump an "idiot."
Woodward reports that after Trump finally condemned white supremacists and neo-Nazis — he initially claimed that "both sides" were to blame for violence during a white supremacist rally last year in Charlottesville, Virginia — he complained to aides, "That was the biggest f---ing mistake I've made."