Ms. Manigault Newman begins the book with Mr. Kelly dismissing her, and suggests throughout that she was weary of the job by the time she departed.

She eviscerates several staff members, particularly Reince Priebus, the president’s first chief of staff, who was trying, with tacit approval from Mr. Trump’s family, to curtail Ms. Manigault Newman’s influence throughout the first year of the administration.

The White House initially declined to respond to the accusations in her book, which is scheduled to be released next week, although several advisers have privately questioned her credibility and have pointed out that she was very upset at being dismissed.

By midday Friday, Mr. Trump ordered the White House to respond.

“Instead of telling the truth about all the good President Trump and his administration are doing to make America safe and prosperous, this book is riddled with lies and false accusations,” the press secretary, Sarah Huckabee Sanders, said in a statement. “It’s sad that a disgruntled former White House employee is trying to profit off these false attacks, and even worse that the media would now give her a platform, after not taking her seriously when she had only positive things to say about the president during her time in the administration.”

In the book, Ms. Manigault Newman writes that Lara Trump, the wife of Mr. Trump’s son Eric — the de facto campaign manager for the next race — called to offer her a $15,000 monthly contract in exchange for her silence on anything negative about the president.

“If you come on board, we can’t have you talking about that stuff,” she writes that Ms. Trump said, adding, “Everything is positive, right?” Within a day, Ms. Manigault Newman says, she received the contract and a nondisclosure agreement preventing her from talking about anything related to the Trump family or Vice President Mike Pence’s family in perpetuity.

“I declined the offer,” she writes. “I was done with Trumpworld.”

Another time, she writes, she walked into the Oval Office with Michael D. Cohen, her friend and the president’s former personal lawyer, and watched as Mr. Trump chewed up a piece of paper that he wanted to keep secret.