Speaking to the Council of Europe in Strasbourg via video link, he said a set of "common standards" would be needed to prevent widespread surveillance programmes like that carried out by the US National Security Agency.
The whistleblower, who lives in Moscow after being granted asylum by Russia, was speaking to officials from across Europe who are investigating mass surveillance.
"I believe the international community should agree to new common standards of behaviour, perhaps a Convention on mass surveillance," he told the council.
"This is not just a problem for the United States and the European Union: this is in fact a global problem", he said.
Snowden, now aged 30, said that the system developed by the NSA was used not just for the prevention of terrorism, but to "follow people, even for non-violent offences" and "without the issue of any judicial warrant".
Such monitoring "represents the most significant new threat to civil rights in modern times," he told the council.
Following the revelations, President Barack Obama was forced to propose changes to the electronic surveillance of US citizens, including proposals put forward last month to take bulk phone data collection out of the hands of the NSA.
Although officials have defended the methods as necessary for national security, the scale of the NSA's surveillance sparked a wave of controversy on both sides of the Atlantic.
Separately today, the European Court of Justice in Luxembourg ruled that the bloc's data-retention law governing phone calls and electronic data was illegal, saying in its current form it was disproportionate and overly-intrusive.
Despite being exiled from his home country, Snowden said he was happy to have started a debate about online surveillance -- which he believes still has a long way to go.
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