"This absurd news was immediately refuted by the family of the well-known presidential candidate," Kremlin spokesman Dmitry Peskov told journalists, referring to Trump's eldest son, Donald Trump Jr.
"We are still seeing attempts to obsessively use the topic of Russia during the US electoral campaign," Peskov complained.
"Unfortunately Russia is being used in the electoral campaign in the US. Unfortunately this traditional game is continuing.
"We think that's not very good for bilateral relations but we understand that we need to get through this unfavourable period."
Russian Foreign Minister Sergei Lavrov earlier shrugged off the accusations by the Hillary Clinton campaign that Russia was involved in the embarrassing leak of emails.
Ahead of meeting US Secretary of State John Kerry in Laos, Lavrov said simply: "I don't want to use four-letter words.