"At this point they need to either stop talking about this or finally present some sort of proof. Otherwise this looks extremely scurrilous," Putin's spokesman Dmitry Peskov told journalists during a visit to Japan.
Obama on Thursday warned that the United States would take action against Moscow after the White House accused Putin of direct involvement in cyber attacks designed to influence the US election.
"I think there is no doubt that when any foreign government tries to impact the integrity of our elections that we need to take action," Obama told NPR radio.
"And we will, at a time and place of our own choosing."
The outgoing US president's remarks dramatically upped the stakes in a dispute between the world's leading nuclear powers over interference that may have swayed last month's tight election in which Republican billionaire Donald Trump defeated Democrat Hillary Clinton.
Obama's threat came after the White House ratcheted up allegations over the Russian hacking by personally tying Kremlin strongman Putin to the attacks.
"I don't think things happen in the Russian government of this consequence without Vladimir Putin knowing about it," one of his top advisers, Ben Rhodes, said earlier Thursday.
Pointing the finger at the Russian president over meddling in the election also puts the White House on a collision course with Trump, who has become increasingly isolated in questioning Russian involvement in hacks of Democratic Party emails that appeared to slow the momentum of Clinton's campaign.
Obama is expected to be peppered with questions about the dispute and any subsequent action when he holds a news conference Friday at 2:15 pm (1915 GMT) before leaving for a vacation in Hawaii.