The documentary follows on the heels of Putin's interview in this week's debut of NBC News' Sunday Night With Megyn Kelly, as controversy swirls in the U.S. over alleged Kremlin meddling in the 2016 presidential elections and ties to President Donald Trump.
In between some of the Russian president's more "bonkers" beliefs, as the Daily Beast puts it, Stone does talk to Putin about Russia's views on North Atlantic Treaty Organisation and the United States.
The interview will air in four parts next week on American premium TV subscription service, Showtime.
Russian President Vladimir Putin says if the United States and Russia made a decision to use their nuclear weapons in a potential conflict with one another, no one would survive that war to claim victory.
But asked if he'd take a shower in a submarine next to a gay man, the Russian leader replied, laughing: "Well, I'd prefer not to shower with him".
'Presidents come and go, and even the parties in power change, but the main political direction does not change, ' Putin said.
Putin dismisses US claims about Trump, Russia and elections
He accused the U.S. media of sensationalizing information and using it as a "weapon of war" against Trump. Putin then appeared to defend President Donald Trump by saying, "You created a sensation out of nothing".
But just to be clear, to show he's not a bigoted homophobe who "cackles" because gay people make him nervous, Putin insists, "that doesn't mean that there should be any persecutions against anyone".
Many criticised Kelly's interview for not pressing Putin hard enough on some of his accusations - which included a claim that the United States had possibly orchestrated the assassination of President John F Kennedy.
Vladimir Putin has spoken about showering next to a gay man.
"I'm not a journalist", Stone said.
"We have to aim our missile systems at facilities that are threatening us", he tells Stone. "I'm interested in preventing a further deterioration in relations".
He told filmmaker Oliver Stone that he doesn't suffer from "natural cycles" getting him down. "I can't think of anything more that I could have said or done". However, on the heels of Putin's combative and testy interview with Megyn Kelly, Showtime's releasing more information about The Putin Interviews via sneak previews with various media outlets.
No country on earth would survive should the world's most powerful nuclear states unleash their atomic weapons, Vladimir Putin has said.