The allegations were part of the classified report presented to outgoing US President Barack Obama and his successor Trump last week by the heads of four premier US intelligence agencies, including FBI and CIA. They were part of the report on Russian interference in the 2016 polls, reports said.
Trump responded by describing the news as fabricated.
A senior US official, with access to the document, said the allegations were presented at least in part to underscore that Russia appeared to have collected embarrassing information on both major candidates but released only material that might harm Democratic nominee Hillary Clinton.
This is a reflection of Russian motivation that bolstered US spy agencies' conclusion that Moscow sought to help Trump win the presidential election, the daily said.
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The two-page synopsis further claimed that there was a continuing exchange of information during the campaign between Trump surrogates and intermediaries for the Russian government, a CNN report said.
BuzzFeed also released a copy of the 35-page report.
"The document was prepared for political opponents of Trump by a person who is understood to be a former British intelligence agent," the website said.
Russia, however, denied claims that it had gathered compromising information on Trump.
"The Kremlin does not have compromising information on Trump," President Vladimir Putin's spokesman Dmitry Peskov told journalists in Moscow.
Peskov also denied allegations that the Kremlin gathered compromising information on Clinton. The Kremlin spokesman described the dossier as "pulp fiction."
After Russia's rebuttal, Trump again tweeted, saying, "Russia just said the unverified report paid for by political opponents is 'A COMPLETE AND TOTAL FABRICATION, UTTER NONSENSE.' Very unfair!".
"Russia has never tried to use leverage over me. I HAVE NOTHING TO DO WITH RUSSIA -- NO DEALS, NO LOANS, NO NOTHING!" he said.
"I win an election easily, a great 'movement' is verified, and crooked opponents try to belittle our victory with FAKE NEWS. A sorry state!" Trump said, as he blasted the media reports.
"It's so ridiculous on so many levels. Clearly, the person who created this did so from their imagination or did so hoping that the liberal media would run with this fake story for whatever rationale they might have," he said.
The New York Times said the uncorroborated summary says that Russia had salacious information about Trump.
It is based on memos generated by political operatives seeking to derail Trump's candidacy.
Earlier, a declassified intelligence report released on Friday has concluded that Russian President Vladimir Putin ordered an "influence campaign," that included hacking of Democratic party groups, in an effort to help Trump's electoral chances by discrediting Clinton in the 2016 presidential campaign.