Dmitry Peskov, President Vladimir Putin’s spokesman, said the allegations were “pulp fiction” and a “clear attempt to damage relations”, the BBC reports.
The unsubstantiated claims say his presidential campaign secretly communicated with Moscow. They also say Russia has information about the US president-elect involving prostitutes.
Trump has condemned the reports.
The president-elect tweeted: “FAKE NEWS – A TOTAL POLITICAL WITCH HUNT!”
Later on Wednesday, he went on to write: “Russia has never tried to use leverage over me. I HAVE NOTHING TO DO WITH RUSSIA – NO DEALS, NO LOANS, NO NOTHING!”
Trump is due to hold a news conference on Wednesday, nine days before he takes office.
It was meant to be about his attempts to separate himself from his business commitments, to address concerns about conflicts of interest.
But it now comes at an awkward time for the Republican president-elect.
Last week, US intelligence agencies released an unclassified report saying Russia ran a hacking campaign to influence the US presidential elections.
Separate reports circulating in US media now say Moscow has damaging information about the president-elect’s business interests and salacious video evidence of his private life.