He says claims that Russia has the power to blackmail him are an attempt by his "crooked opponents" to "belittle" his victory.
Spy agencies should not have allowed claims that Russia has compromising intelligence on him to be leaked, Donald Trump has said.
The dossier reportedly alleges Russia obtained compromising material on the President-elect during a stay in a five-star hotel in Moscow - including recordings of graphic sexual acts.
The unsubstantiated document - reportedly compiled by a retired British spy - was dismissed by Mr Trump as "fake news" on Wednesday.
In a series of fresh tweets, the real estate mogul said: "Russia has never tried to use leverage over me. I HAVE NOTHING TO DO WITH RUSSIA - NO DEALS, NO LOANS, NO NOTHING!"
He went on: "I win an election easily, a great "movement" is verified, and crooked opponents try to belittle our victory with FAKE NEWS. A sorry state!
"Intelligence agencies should never have allowed this fake news to "leak" into the public. One last shot at me.Are we living in Nazi Germany?"
Intelligence chiefs have reportedly been unable to verify the claims, which Russia has dismissed as "utter nonsense".
The Kremlin earlier rushed to the billionaire's defence and rejected claims that it had in its possession embarrassing personal and financial information to blackmail Mr Trump with if necessary.
"It is an attempt to damage our bilateral relations, it is pulp fiction," said Russian President Vladimir Putin's spokesman Dmitry Peskov.
"You have to react to this with a certain humour, but there's also a sad side to this. Hysteria is being whipped up to maintain a political witch hunt.
"The Kremlin does not engage in collecting compromising information."
Russian state television questioned the timing of the leak - which is said coincided with President Barack Obama's farewell address in Chicago.
President Obama and Mr Trump were briefed on the dossier last week.
Mr Trump is likely to face questions about it when he gives a news conference - planned before the report was made public - this afternoon at Trump Tower in New York.
His pick for Secretary of State, Rex Tillerson, is also expected to be grilled later by senators at his confirmation hearing over his close business relationship with Mr Putin.