Joseph Gordon-Levitt, Shailene Woodley and Oliver Stone in San Sebastian Photo: Courtesy of San Sebastian Film Festival/Pablo Gómez
Noting that his film shows Obama on TV in his first term, advocating transparency and an end to illegal wiretaps, Stone added: "He went the opposite way.
"Mr Snowden and Lindsay were both hoping that he would change course because he seems like a man of great integrity. However, five years later, Mr Snowden did what he did because he knew that, on the contrary, Mr Obama had doubled down on the Bush administration policy. It's a much more severe state, he's gone after eight whistleblowers under the espionage act and he's created, by 2016, the most massive global security state that has ever been seen or can be conceived. Way beyond the East German Stasi."
Despite this, Stone insisted that the film had "no agenda".
He said: "First of all I'd like to say that movie was planned two years ago so it has nothing to do with these next elections. We had no intention of coming out in the middle of them, none at all, so there's no agenda here at all. Secondly, neither candidate has talked about the surveillance state nor, much less, Edward Snowden. Neither of them in past statements have indicated they would have any mercy on this case. I think the best hope, right now, is in President Obama who has a few more months in office. I think in his infinite sense of respect and mercy, he would grant a pardon."
Joseph Gordon-Levitt: 'I spent about four hours sitting with Ed as well as his long-time girlfriend Lindsay and the three of us spoke at length'
"It is the death knell of true liberty and it's the beginning of authoritarianism and tyranny. It's a very dangerous thing you say. Terrorism can be fought and I agree it is a horrible thing but it is not the most dangerous thing to ever visit mankind.
"There has been great danger throughout history. So in the name of one thing, like terrorism, to change all the rules is, to me, not a marginal response, it is an extreme response. Let's beware of fascists and tyrants who take over our governments and tell us, 'We are going to protect you.' I don't want that kind of protection.
"They say that with mass eavesdropping on everyone in the world they can give us security - they haven't. 9/11 - there are so many flaws in the state that we have there. They didn't do the job. The NSA missed the signals that they had but they didn't know what they had because they had too much. The FBI really screwed up, the CIA screwed up. It didn't work in the Iraq War, they said there were weapons of mass destruction, there weren't. This is our Intelligence - it doesn't seem so intelligent to me. They passed all these extreme laws. Beware of these extremities."
The director - who was awarded a lifetime Donostia award by the festival in 2012 - said he travelled to Moscow nine times to speak to Snowden and met Mills twice, while developing the movie. Woodley said she also benefited from speaking to Snowden's partner.
Woodley, Stone and Gordon-Levitt on the red carpet Photo: Courtesy of San Sebastian Film Festival/Montse Castillo
"You don't have to agree with what he did or disagree with what he did but we can all relate to a relationship, to partnership and we can all relate to a deep love."
Gordon-Levitt also talked about how speaking to Snowden had helped him recreate his life in the biopic.
He said: "I spent about four hours sitting with Ed as well as his long-time girlfriend Lindsay and the three of us spoke at length. It was really vital to me because of course I could learn about his politics by reading his interviews and watching documentaries, and Ed himself is always trying to take the attention off his personal life and put it on the issues that he raises. But, of course, because I was going to play him in the movie my focus was on him personally and I could observe those nuances - how he sits or stands, walks or talks, how he shakes your hand or eats his lunch - these little details were really valuable for me as I prepared to play him."
Snowden is on general in the US now and will be screened in the UK at London Film Festival next month