The president-elect said there was a “political witch-hunt” after the US media ran unsubstantiated allegations that Moscow is sitting on embarrassing material about the billionaire.
Intelligence officers briefed the Republican and President Barack Obama about the contents of the document last week.
After reports emerged on US broadcasters, President-elect Trump tweeted “FAKE NEWS - A TOTAL POLITICAL WITCH HUNT!”
Kremlin spokesman Dmitry Peskov said the reports were “complete fabrication and utter nonsense” and insisted the Russian government “does not engage in collecting compromising material”.
The New York Times said the dossier had been drawn up by a former British intelligence officer with extensive experience of Russia during the presidential race. It is said to have been funded by opponents of his White House bid, including Republicans.
It comes after Russia has accused Britain of preparing an “official witch-hunt” against President Vladimir Putin’s administration amid “panic and hysterics” over a loss of control in Europe.
The Russian embassy to Britain posted online an extraordinary attack on the Government, accusing it of planning to brief Mr Trump’s incoming United States administration against Moscow.
Prime Minister Theresa May is preparing for her first meeting with the US president-elect, expected in the spring.
Foreign Secretary Boris Johnson accused Russia of being “up to all sorts of very dirty tricks” such as cyber warfare.
The embassy also speculated the Government was seeking to rerun the Brexit referendum by claiming it was tainted by Russian influence and attacked the British intelligence services.
It directly criticised former MI6 chief Sir Richard Dearlove for standing down from a Cambridge University intelligence forum over fears of Kremlin influence.
The embassy also suggested the UK was being hypocritical when criticising alleged Russian war crimes in Syria, highlighting the use of British-made banned cluster bombs in the civil war in Yemen by a Saudi-led coalition.
And it claimed Britain had once again “outsourced” the fight against extremism to Russia.
“Ultimately, defeating Nazi Germany was ‘outsourced’ to the Soviet Union,” the post said.