"They need to either stop talking about this or finally present some sort of proof," Russian President Vladimir Putin's spokesman said.
On Friday, Hillary Clinton said Mr Putin ordered the hack because he had a "personal beef" against her.
President Barack Obama has vowed to take action against Russia for its alleged interference.
"We need to take action and we will," he told US public radio network NPR.
Russia stands accused by the US of hacking the emails of the Democratic Party and a key Hillary Clinton aide, which the Kremlin strongly denies.