January 18, 2017 0806 GMT
"This is an evident attempt to harm our bilateral ties," Kremlin spokesman Dmitry Peskov told reporters in Moscow. "The Kremlin does not engage in collecting compromising information."
A US official told AP on Tuesday that intelligence officials had informed Trump about an unsubstantiated report that Russia had compromising personal and financial information about him. The official spoke on the condition of anonymity.
After news reports were published about the briefing, Trump tweeted: "FAKE NEWS – A TOTAL POLITICAL WITCH HUNT!"
Peskov dismissed the report but commented that the allegations could be used to keep American politicians from wanting to improve ties with Russia.
"We should treat it with humor, but there is a sad side to it, too," he said. "There are people who are whipping up this frenzy, who are doing their best to keep this witch hunt going."
Peskov described the report as part of efforts to "keep harming the relations, not allow anyone to think about whether this is in the interests of both countries, the interests of the global community and what can be done to move from a total confrontation to a more constructive approach".
Among the claims included in the reports are that Trump aides were involved with the alleged Russian hack of the Democratic Party of his rival Hillary Clinton during the 2016 presidential election.
Michael Cohen, a lawyer to Trump named in the memos, has denied a specific claim that he went to Prague in August or September 2016 to meet Kremlin representatives to talk about the hacking.