In a tweetstorm Saturday morning ahead of the news conference, the president called himself a "very stable genius" and called being "really smart" one of his greatest assets.
Trump cited his career in business and reality television and his victory in last year's election as evidence of his mental prowess. And he again lashed out at the ongoing special counsel investigation into his campaign's contacts with Russian operatives, calling suggestions that he colluded with Moscow a "total hoax on the American public."
Trump's outburst came a day after the public release of the book by Wolff, who said he spent time in the West Wing interviewing top aides, as well as Trump.
Wolff said he spent a total of three hours talking with Trump during the campaign and after Trump became president, but White House aides said Wolff spoke to Trump only once by phone for about five to seven minutes after he assumed office.
Wolff paints the picture of a president who is unfit for the job and aides who come to fear Trump is not capable of, or interested in, processing information and making important decisions.
Late Friday, Trump blasted Wolff as a "total loser," and the president mocked his former campaign chairman and former White House adviser, Steve Bannon, who was a key source for the book.
Bannon criticised other aides and Trump's son, calling a meeting at Trump Tower last year between Donald Jr. and a Russian lawyer "treasonous."
White House aides have mounted an all-out attack on the book since it was first reported on Wednesday, calling it "fiction" and a "complete fantasy." And Trump's lawyers sent cease-and-desist letters to Wolff and his publisher demanding they not release the book. But the publisher, Henry Holt, moved up the release date from later this month to Friday amid the publicity, and hard copies were quickly sold out in the Washington area.
At Camp David, Trump said Wolff, who has said he has a relationship with Trump, "does not know me at all."
"By the way, he did not interview me," Trump said, though he then said Wolff interviewed him once "a long time ago" about for magazine story.
Trump also criticised Wolff's past reporting, including a book about News Corp. Chairman Rupert Murdoch.
The president said Bannon gave Wolff the most access. "I guess 'Sloppy Steve' brought him into the White House a lot," Trump said of Bannon, who left the White House under pressure in August.
"That's why Sloppy Steve is looking for a job."
Reporters asked White House press secretary Sarah Huckabee Sanders on Thursday to respond to the book's suggestion that Trump is mentally unfit for office.
"It's disgraceful and laughable," she said.
"If he was unfit, he probably wouldn't be sitting there and wouldn't have defeated the most qualified group of candidates the Republican Party has ever seen. This is an incredibly strong and good leader. That's why we've had such a successful 2017 and why we're going to continue to do great things as we move forward in this administration."