Putin has vehemently dismissed the accusations, saying they are meant to distract American voters from domestic problems
"The number of mythical, dreamt-up problems includes the hysteria -- I can't think of another word -- that has broken out in the United States about the influence of Russia on the current elections for the US president," Putin said at a Valdai Discussion Club meeting of political scientists in Sochi.
"Does anyone seriously think Russia can somehow influence the choice of the US people? Is the US some kind of banana republic? The United States is a great power. Please correct me if I'm wrong," Putin said to laughter in the audience.
Washington last week formally accused the Russian government of trying to "interfere" in the 2016 White House race by hacking US political institutions, charges the Kremlin has repeatedly dismissed.
Putin has vehemently dismissed the accusations, saying they are meant to distract American voters from domestic problems.
"It's a lot easier to distract people's attention towards Russia's so-called hackers, spies, agents of influence and so on," Putin said Thursday.
Russian authorities have also slammed Washington for "unprecedented" threats after US Vice President Joe Biden told NBC this month that Putin would receive a "message" over the alleged hacking.
NBC later reported that the CIA was preparing a retaliatory cyber attack "designed to harass and embarrass the Kremlin leadership."
Russia's foreign ministry at the weekend said that an old version of its website had been attacked after a US hacker claimed he broke in and posted a mocking message.
Ministry spokeswoman Maria Zakharova said the incident could indicate that a US "cyber machine of destruction has started acting".
The Kremlin was propelled to the heart of US politics in July after Hillary Clinton's campaign blamed Moscow for a damaging leak of emails from the Democratic National Committee.
Russia has been accused of favouring Republican candidate Donald Trump -- who has praised Putin and called for better relations with Moscow -- over the more hawkish Clinton.
Russia's relations with the United States have slumped to a post-Cold War nadir over the conflict in Ukraine and stalled efforts to end the Syrian war.