President Donald Trump has hit out at “very weak” libel laws in the US as he branded an explosive new book detailing the inner workings of the White House as “fiction”.

Suggesting he would like to see tougher laws on speech, Mr Trump said that if libel laws “were strong... you wouldn’t have things like that happen where you can say whatever comes into your head” – referring to Michael Wolff’s book Fire and Fury: Inside the Trump White House.

The book has caused a storm of controversy and has left the President facing questions about his mental state, with quotes in Fire and Fury – including from Mr Trump’s former chief strategist Steve Bannon - suggesting that even those close to Mr Trump had questioned his capability.

Early on Saturday, Mr Trump wrote a string of messages on Twitter where he rejected such claims, saying he was a “very stable genius” whose two greatest assets are his “mental stability and being, like, really smart”.

Mr Wolff’s new book, which has shot to the top of the bestseller list on Amazon after being released four days early, has clearly riled the President and he used a rare news conference during a retreat with Republican leadership to reinforce what he sees as a stellar list of life achievements.

Answering a question about why he saw the need to tweet about his mental state, Mr Trump said that he had attended “the best college” and was an “excellent” student. He added that he came out of college and “made billions and billions of dollars... [and] became one of the best business people” before touting his “tremendous success” over a decade on television. He went on to add that he ”ran for President one time, and won”.

Mr Trump also called Mr Wolff a “fraud” and the book “a complete work of fiction”, saying that “he doesn’t know me at all” and said that he had not been interviewed in the White House as Mr Wolff had said. He later admitted that he had spoken to Mr Wolff during his presidential campaign.

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The gathering at Camp David, with a number of members of his cabinet, is supposed to be a weekend for Mr Trump to concentrate on their agenda for 2018. Senate Majority Leader Mitch McConnell and House of Representatives Speaker Paul Ryan were also present for the two days of talks, with the Republican party facing a battle to keep control of the US Congress in November’s elections.

At the beginning of his remarks, Mr Trump described having some “incredible meetings” with colleagues, saying the party was readying its 2018 legislative agenda.

He said the group, 10 of whom were on stage with him, the only woman being Secretary of Homeland Security Kirstjen Nielsen, discussed a variety of topics, from national security and infrastructure to the military and the budget.

Mr Trump said: “We are very well prepared for the coming year.” He added that his administration ”finished very strong,” referring to the passing of a tax reform bill in December that marked the biggest overhaul of the tax code in nearly three decades.

However, with the President taking a number of questions from the assembled journalists – another rarity for Mr Trump – attention soon turned back to Mr Wolff’s book.

A lawyer for Mr Trump had sent a letter calling for its publisher not to release the book – but it did so anyway about a day later.

Mr Trump has labelled Mr Bannon ”sloppy Steve”, and issued a furious statement over his quotes in Fire and Fury earlier in the week after a number of reports appeared about the contents of the book. The President continued in that vein as he spoke about Mr Wolff while answering the question about his mental state.

“I don’t know this man. I guess sloppy Steve brought him in the White House quite a bit and it was one of those things. That’s why sloppy Steve is now looking for a job,” Mr Trump said.

In one of his morning tweets, the President said critics were “taking out the old Ronald Reagan playbook and screaming mental stability and intelligence.” Mr Trump added that going from successful businessman to reality TV star to President on his first try “would qualify as not smart, but genius .... and a very stable genius at that!”

Former President Reagan died in 2004, at age 93, from pneumonia complicated by the Alzheimer’s disease that had progressively clouded his mind. At times during his time in the White House Mr Reagan would appear to lose his train of thought, but his diagnosis came years after he left the Oval Office.

White House Chief of Staff John Kelly told reporters at Camp David that Mr Trump did not seem angry about the book and on Friday night had watched a new film, The Greatest Showman about legendary circus promoter P T Barnum, with Republicans and his cabinet.

Once beyond the issue of Mr Wolff during his news conference, Mr Trump opened up about a number of other topics. The President said he would “absolutely” be willing to talk on the phone to North Korean leader Kim Jong Un and that he hopes a positive development results from talks between North Korea and South Korea.

Pyongyang agreed on Friday to hold official talks with South Korea next week, the first in more than two years, hours after Washington and Seoul delayed a military exercise amid a standoff over the Kim regime’s nuclear and missile programmes.

The talks between North Korea and South Korea are expected to cover the Winter Olympics, to be held in South Korea next month, and inter-Korean relations.

“Look, right now they’re talking Olympics. It’s a start, it’s big start. If I weren’t involved they wouldn’t be talking at all right now,” Mr Trump said, but made clear his stance. Mr Kim “knows I’m not messing around. I’m not messing around. Not even a little bit, not even 1 per cent. He understands that,” he said.

“If something can come out of those talks, that would be a great thing for all of humanity, that would be a great thing for the world,” he added.

Mr Trump has given Congress until March to come up with legislation to protect hundreds of thousands of young people brought to the country illegally, who have been shielded from deportation and given the right to work under the Deferred Action for Childhood Arrivals (DACA) programme he has phased out.

Talking about the issue on Saturday, Mr Trump said he would not sign such legislation – a priority for Democrats - unless Congress agrees to overhaul the legal immigration system.

He said any deal must include an overhaul of the family-based immigration system as well as an end to the diversity visa lottery, which draws immigrants from under-represented parts of the world

“We all want DACA to happen, but we also want great security for our country,” he added.

Moving onto the mid-term elections in November, Mr Trump says he would be “very involved” with both House and Senate races, and will campaign for incumbents and “anybody else that has my kind of thinking.”