At an ill-tempered news conference, he said if spies had given the unsubstantiated documents to the media it would be a "tremendous blot on their record".
He later went further, saying: "I think it was disgraceful, disgraceful that the intelligence agencies allowed any information that turned out to be so false and fake out there.
"That's something that Nazi Germany would have done."
But the White House said his criticism of intelligence officials was "deeply misguided".
The alleged source of the dossier containing allegations about Mr Trump has been named by US media as former British spy Christopher Steele.
There had been restrictions in place on publishing the identity of a former MI6 officer, which have since been lifted.
The documents - apparently gleaned from sources in Russia and the US - claim the Russian regime has been "cultivating, supporting and assisting" Mr Trump for at least five years.
The US President-elect, who is due to be inaugurated next week, dismissed the salacious claims in the 35-page document as "nonsense", "fake news" and "phoney stuff".
He told reporters: "It was a group of opponents that got together, sick people, and they put that c**p together."
The unverified documents, consisting of memos, reportedly allege Russia obtained compromising material on him during a stay in a five-star hotel in Moscow - including recordings of graphic sexual acts.
At the news conference in New York - intended to focus on how he will hand his business empire to his sons - Mr Trump turned on a CNN reporter for the "terrible" organisation "building the story up".
Journalist Jim Acosta stood up and said: "Since you are attacking us can you give us a question?"
Despite several requests, Mr Trump dismissed the journalist, saying "not you, you are fake news".
The dossier containing the claims was published by BuzzFeed and Mr Trump said it would "suffer the consequences".
CNN said its own decision to publish "carefully sourced reporting" on the documents was "vastly different than BuzzFeed's decision to publish unsubstantiated memos".
Sources in the memos claimed Russian authorities had obtained enough embarrassing evidence of Mr Trump's conduct while staying in the country to be able to blackmail him if necessary.
The documents were also said to have included allegations of close contact between associates of Mr Trump and Russians about hacking into Democratic party emails and colluding to win the presidential election.
The documents - apparently gleaned from sources in Russia and the US - claim the Russian regime has been "cultivating, supporting and Russia has rejected the allegations as "utter nonsense", while the US tycoon said he has no dealings with or in Russia.
But he said he did believe Russia was behind hacking during the White House race, although he added other countries, including China, have also hacked the US.
On Twitter, he claimed there was a political "witch hunt" against him.
The allegations have not been verified by intelligence chiefs, but they reportedly considered them sufficiently serious to tell him about them in a two-page synopsis during a wider briefing recently on Russian hacking.
Former CIA operative Evan McMullin said he had warned the media in September that Mr Putin could be blackmailing Mr Trump but that he "was mostly dismissed at the time".
He told Sky News: "If you're a person of influence and you travel to Moscow, you should assume you are being watched when you are in your hotel room. This is something the Russians do."