Donald Trump has dismissed allegations he is unfit to be president, proclaiming himself to be a "very stable genius" in a series of tweets.

The US president's Twitter tirade on Saturday comes after the publication of an explosive new book on the Trump administrative that claims Oval Office staff believe he is not fit to hold office.

In reply, Mr Trump said two of his "greatest assets have been mental stability and being, like, really smart".

In his latest online onslaught, Mr Trump accused his critics of trying to make an issue of his "mental stability and intelligence".

"Now that Russian collusion, after one year of intense study, has proven to be a total hoax on the American public, the Democrats and their lapdogs, the Fake News Mainstream Media, are taking out the old Ronald Reagan playbook and screaming mental stability and intelligence," he wrote in a series of trademark tweets.

"Actually, throughout my life, my two greatest assets have been mental stability and being, like, really smart. Crooked Hillary Clinton also played these cards very hard and, as everyone knows, went down in flames.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!"

The publication of Fire and Fury: Inside the Trump White House by Michael Wolff has already provoked a very public rift with his former strategist, Steve Bannon, who was one of the main sources of the book.

Responding to claims the president has a short attention span, regularly repeats himself and refuses to read briefing notes, secretary of state Rex Tillerson told CNN that he had "no reason to question his mental fitness."

But despite defending Mr Trump, Washington's chief diplomat admitted the president has a very different decision making process and Mr Tillerson has spent a lot of time "understanding how to best communicate with him."