The US President wrote: “Michael Wolff is a total loser who made up stories in order to sell this really boring and untruthful book.
“He used Sloppy Steve Bannon, who cried when he got fired and begged for his job.
“Now Sloppy Steve has been dumped like a dog by almost everyone. Too bad!”
The book – Fire And Fury by Michael Wolff – quotes White House aides claiming Mr Trump has a short attention span, often repeats himself and that he refuses to read briefing notes.
Wolff said many of those close to Mr Trump describe him as a “moron”, an “idiot” and “like a child”.
Wolff told NBC: “They all say he is like a child.
“And what they mean by that is he has a need for immediate gratification. It’s all about him… they say he’s a moron. An idiot.”
Wolff claims Mr Trump’s former ally and chief strategist Steve Bannon questioned his fitness for office.
Mr Bannon was sacked by Mr Trump in August.
Meanwhile, US Secretary of State Rex Tillerson defended Mr Trump’s mental fitness, responding to claims in the book.
In an interview with CNN, Mr Tillerson responded: “I’ve never questioned his mental fitness. I’ve had no reason to question his mental fitness.
“He is not a typical President of the past, I think that’s well-recognised. That’s also why the American people chose him.”
The relationship between Mr Tillerson, a former oil executive, and Mr Trump has not always been strong but, in response to rumours he may be shown the door, Mr Tillerson said: “I intend to be here for the whole year.”
Last year, he reportedly described the President as a “moron” after a national security meeting, a claim denied by his office.
According to the book, the President is regarded as an “idiot” by treasury secretary Steve Mnuchin and former chief of staff Reince Priebus.
Mr Trump’s lawyers tried to block publication of the book, before publishers brought the release date forward.
Wolff also says Mr Trump, 71, did not want to win the 2016 presidential election because losing would offer “a far more powerful brand and untold opportunities”.
But Press Secretary Sarah Huckabee Sanders said this was “ridiculous”, adding that Mr Trump and his family “would not have put themselves through” the campaign if they did not want to win.
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Wolff said he spoke to Mr Trump after his inauguration and “spent about three hours with the President over the course of the campaign in the White House, so my window into Donald Trump is pretty significant”.
He added: “I spoke to people who spoke to the President on a daily, sometimes minute-by-minute basis.”