US President Donald Trump has rejected an author's withering accusations that he is mentally unfit for office, saying his track record shows he's "a very stable genius".

Key points: Trump says Wolff's book is "a complete work of fiction"

Trump says Wolff's book is "a complete work of fiction" Says his greatest assets are his mental stability and being "really smart"

Says his greatest assets are his mental stability and being "really smart" Wolff says he believes Trump is unfit for office

Michael Wolff, who was granted unusually wide access to the White House during much of the President's first year, has painted a picture of Mr Trump as an inept, sexist, narcissistic man leading a dysfunctional administration.

Mr Trump, in a series of morning tweets, said his Democratic critics and the US news media were bringing up the "old Ronald Reagan playbook and screaming mental stability and intelligence" since they had not been able to bring him down in other ways.

Reagan, a Republican who was the US president from 1981-1989, was diagnosed with Alzheimer's disease in 1994 and died in 2004.

"Actually, throughout my life, my two greatest assets have been mental stability and being, like, really smart," Mr Trump tweeted.

"I went from VERY successful businessman, to top T.V. Star … to President of the United States (on my first try).

"I think that would qualify as not smart, but genius.... and a very stable genius at that!"

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Mr Trump, 71, made the comments from the presidential retreat at Camp David, Maryland, where he also said he would be open to talking directly with North Korean leader Kim Jong-un, and took credit for the upcoming talks between South Korea and the North.

He told reporters Wolff is a "fraud" and repeated earlier remarks that the book, Fire and Fury: Inside the Trump White House, is "a complete work of fiction".

"I think it's a disgrace," he said.

Mr Trump blamed former adviser Steve Bannon, who he called "Sloppy Steve," for granting Wolff access at the White House, and said Wolf does not know him "at all".

"I went to the best college … I was a very excellent student, came out, made billions and billions of dollars, became one of the top business people, went to television and for 10 years was a tremendous success — as you probably have heard — ran for President one time and won," he said.

"And then I hear of this guy that does not know me, doesn't know me at all — by the way, did not interview me — he said he interviewed me for three hours in the White House.

"It didn't exist, OK. His imagination."

Mr Trump said his critics were bringing up the "old Ronald Reagan playbook". ( Reuters: Yuri Gripas )

The tweets were another sign of Mr Trump's frustration at what he views as unfair treatment by the news media of his presidency amid the Russia probe.

Mr Trump, asked about a New York Times report that his aides had pressured Attorney-General Jeff Sessions not to recuse himself from the Russia investigation, said: "Everything I've done has been 100 per cent proper."

White House chief of staff John Kelly told reporters at Camp David that he had not been aware of Mr Trump's morning tweets.

Mr Kelly said Mr Trump did not seem angry and on Friday night (local time) had watched a new movie, The Greatest Showman, about legendary circus promoter PT Barnum, with other politicians at the retreat.

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Trump like 'a pinball, just shooting off the sides'

Wolff's book has proved to be another shock to the system for Mr Trump and his top aides, coming just as he starts his second year in office.

Wolff has repeatedly said he believes Mr Trump is unfit for office, and told NBC News that White House staff around Mr Trump treated him like a child.

"The one description that everyone gave, everyone has in common — they all say he is like a child," Wolff said.

"And what they mean by that, he has a need for immediate gratification. It's all about him."

"This man does not read, does not listen. He's like a pinball, just shooting off the sides."

White House officials and Mr Trump's high-profile supporters have launched an effort to raise doubts about Wolff's credibility.

White House spokesman Sarah Huckabee Sanders said earlier in the week that the book includes "mistake after mistake after mistake".

Sorry, this video has expired White House says book on Trump 'disgraceful and laughable'

Fox News correspondent Geraldo Rivera told Fox and Friends he had spoken to Mr Trump on Friday and that he was "very, very frustrated" that the issue of his mental fitness was getting traction.

Mr Trump is to undergo a physical examination on January 12, the first of his presidency.

The exam was announced on December 7 after questions arose about Mr Trump's health when he slurred part of a speech announcing that the United States recognised Jerusalem as the capital of Israel.

Reuters