U.S. President Donald Trump on Saturday rejected an author's accusations that he is mentally unfit for office and said his track record showed he is a "stable genius."

Michael Wolff, who was granted unusually wide access to the White House during much of Trump's first year, has said in promoting his book, "Fire and Fury - Inside the Trump White House," that Trump is unfit for the presidency.

Trump, in a series of extraordinary morning posts on Twitter, said his Democratic critics and the U.S. news media were bringing up the "old Ronald Reagan playbook and screaming mental stability and intelligence" since they have not been able to bring him down in other ways.

Reagan, a Republican who was the U.S. 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," said Trump, a former reality TV star.

"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!"

Trump, 71, issued the tweets from the presidential retreat at Camp David, Maryland, where he was meeting Republican congressional leaders and many Cabinet secretaries about their legislative agenda for the year.

The tweets were another sign of Trump's frustration at what he views as unfair treatment by the news media of his presidency amid a federal investigation into whether he or his campaign aides colluded with Russia during the 2016 presidential campaign, in which he defeated Democrat Hillary Clinton.

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

Wolff told BBC Radio in an interview broadcast on Saturday that based on his interviews with the people around Trump that he believed the president was unfit for office.

READ: Trump book author says his revelations will bring down U.S. president

He told NBC News on Friday that White House staff treated Trump 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."

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

Trump is to undergo the first physical examination of his presidency on Jan. 12. The exam was announced on Dec. 7 after questions arose about Trump's health when he slurred part of a speech announcing that the United States recognised Jerusalem as the capital of Israel.

White House officials and Trump's high-profile supporters have launched an effort to raise doubts about Wolff's credibility. White House spokesman Sarah Sanders said earlier in the week that the book includes "mistake after mistake after mistake."