"That's something that Nazi Germany would have done," he said.
He was replying to unsubstantiated allegations that his election team colluded with Russia and there were salacious videos of his private life.
Intelligence agencies considered the claims relevant enough to brief both Mr Trump and President Obama last week.
Mr Trump also said for the first time that he accepted Russia was behind hacking attacks that took place during the presidential campaign.
In his first briefing as president-elect, Mr Trump also confirmed he was handing total control of his businesses to his two sons.
The claims - how and why?
Trump's briefing a theatre of the absurd
Did Trump answer our questions?
Full transcript of press conference
The press conference was scheduled in order for Mr Trump to give details about his business affairs but was dominated by the allegations of compromising material.
Mr Trump said the information "should have never been written and certainly should never have been released".
"It's all fake news, it's phoney stuff, it didn't happen," he said, adding that "sick people" had "put that crap together... it's an absolute disgrace".
Mr Trump said he could not talk about what he had heard in last week's intelligence agency briefing but said there had been "many witnesses" there and that it would be a "tremendous blot" on the reputation of intelligence agencies if they had been responsible for leaking the details.
He added later in the briefing: "I think it was disgraceful - disgraceful that the intelligence agencies allowed any information that turned out to be so false and fake out. I think it's a disgrace... and that's something that Nazi Germany would have done and did do."
In response White House spokesman Josh Earnest said it was "deeply misguided for anybody, at any level, to question the integrity and motives of the patriots" in the nation's intelligence agencies.
'Pile of garbage'
A 35-page dossier of allegations has been published in full on Buzzfeed and reported by CNN.
Mr Trump called Buzzfeed a "failing pile of garbage" and accused CNN of "going out of their way to build it up".
He refused to take a CNN reporter's question at the press conference. CNN later defended its decision to publish what it called "carefully sourced reporting", saying it was "vastly different from Buzzfeed".
The allegations claim Russia has damaging information about the president-elect's business interests, and salacious video evidence of his private life, including claims of using prostitutes at the Ritz-Carlton hotel in Moscow.
Denying any such claims, Mr Trump said that as a high-profile person he was extremely cautious about all that he did when travelling abroad.
Russia also strongly denied the allegations.
Dmitry Peskov, President Vladimir Putin's spokesman, said they were "pulp fiction" and a "clear attempt to damage relations".
The president-elect was also asked about the hacking scandal that dominated the US election campaign, with US spy agencies concluding Russia was behind the hacking of Democratic Party emails.
Mr Trump said for the first time "I think it was Russia", but added that "we get hacked by other people".
He said: "We talk about the hacking and hacking's bad and it shouldn't be done."
But he added: "Look at the things that were hacked, look at what was learned from that hacking... Hillary Clinton got the questions to the debate and didn't report it."
Mr Trump did not answer directly when asked whether his team had communicated with Russia during the election campaign but he did say that any hacking by Mr Putin must stop. "He shouldn't be doing it. He won't be doing it."
Other areas of the briefing:
Mr Trump said he had formally handed "complete and total" control of his business empire to sons Don Jr and Eric to avoid any conflict of interest, adding: "They're not going to discuss it with me"
The president-elect said there would be "a major border tax" on companies moving from the US to other nations
David Shulkin was selected to head Veterans Affairs
A plan was to be submitted "essentially simultaneously" to both repeal and replace Barack Obama's affordable health care programme Obamacare
The wall to be built on the Mexican border would start as soon as possible with US funding but Mr Trump added: "Mexico in some form... will reimburse us"
Donald Trump's team
'Never been to Prague'
Before the briefing, the Trump team acted to dismiss news of the compromising material.
Michael Cohen, a lawyer to Mr Trump named in the 35-page dossier, denied a specific claim that he went to Prague in August or September 2016 to meet Kremlin representatives to talk about the hacking.
"I've never been to Prague in my life. #fakenews," he tweeted.
US media suggest the alleged salacious videos were prepared as kompromat - a Russian acronym for compromising materials.
How this came to light
The allegations began circulating in political and media circles in recent months.
The BBC understands they are based on memos provided to an independent organisation opposed to Mr Trump by a former member of Britain's MI6, Christopher Steele.
Mr Steele is a director of Orbis - which describes itself as a leading corporate intelligence company. He did not respond to a request for comment.
Sources say the CIA regards the memos as "credible". The original intention was to derail Mr Trump's candidacy, reports say.
The BBC first saw the documents in October but has been unable to verify the claims included. Several material inaccuracies have been highlighted.
However, past work by the British operative was considered by US intelligence to be reliable, US media say.
The existence of the documents was first reported by Mother Jones in October.(BBC)