"If we want to have a better world, we cannot hope for an Obama and we should not fear a Donald Trump. Rather we should build it ourselves," Snowden said late Thursday, addressing an audience in the Netherlands in a live video chat from Russia.
While he said Trump's victory in Tuesday's US presidential elections was "a dark moment" in American history, he insisted the bigger question was "how do we defend the rights of everyone, everywhere, without regard to borders?"
Snowden leaked thousands of classified documents in 2013 revealing the vast US surveillance of private data put in place after the September 11, 2001 attacks.
Snowden appeared Thursday via an encrypted live video stream at a cinema in Amsterdam ahead of the Dutch premiere of director Oliver Stone's new movie about his life.
"I try not to look at this as a question of a single election or a single president or even a single government, because we see these threats coming across borders," Snowden said.
He highlighted Moscow's "Big Brother" law passed earlier this year forcing online companies to store users' data and pass it to government agencies if requested, as well as China's new mass surveillance law.
"This is a dark moment in our nation's history, but it is not the end of history," Snowden said,
"If we work together we can build something better and we can enjoy a more free and a more liberal society that benefits everyone."
Snowden, 33, is wanted in the United States to face trial on charges brought under the tough Espionage Act. But he said he was unconcerned about the possibility that Russian President Vladimir Putin could send him back once Trump is sworn in.
Although it would "be crazy to dismiss" the idea that Putin could strike a deal to extradite him, Snowden said he would have remained in Hawaii if he had been concerned about his own safety.
"While I obviously care about what happens to me, I am the least important part of any of this. This is not about me, this is about us," he said.
It was more important to focus on resisting the "civic dangers to everyone" rather than on individual cases.
Snowden has repeatedly said he would be prepared to return to the US if he is allowed to address a jury and tell them why he did what he did, saying he remained "proud" of his actions. But that is denied to him under the restrictions of the Espionage Act.