In a resolution on Thursday, EU lawmakers called on the bloc's 28 member states to grant protection to Snowden as a "human rights defender" after he blew the lid on the US government's mass surveillance programmes.
On Twitter, Snowden said the vote was "extraordinary" and a "game-changer".
"This is not a blow against the US government but an open hand extended by friends. It is a chance to move forward," he said in one tweeted message.
MEPs urged member states to "drop any criminal charges against Edward Snowden, grant him protection and consequently prevent extradition or rendition by third parties, in recognition of his status as whistle-blower and international human rights defender."
The vote in the European Parliament has no legal force, as questions of asylum and immigration are decided at the national level. However, the motion has encouraged Danish politicians who want Denmark to support the renegade NSA operative.
On Friday, Danish political parties The Alternative and the Red-Green Alliance (Enhedslisten) said that they want parliament to vote on offering the 32-year-old American asylum in Denmark.
“Snowden is a democratic hero and it is fantastic that the EU has now gone in front and is holding democracy’s banner high,” Alternative MP Uffe Elbæk said in a statement.
Elbæk was behind an unsuccessful 2014 attempt to get parliament to offer Snowden asylum in Denmark but he said that the parliament's resolution means that it’s time to take up the matter again.
“I would be incredibly proud of Denmark if we were the European country to offer Edward Snowden asylum,” he said.
The Red-Green Alliance also supports bringing a new proposal before parliament.
“Edward Snowden has revealed that the American intelligence service has spied on European governments and carried out mass surveillance of the European people so it is in our own interest to protect a brave man like Snowden,” party spokeswoman Pernille Skipper told Berlingske’s Politiko.
According to Politiko, a packed parliamentary schedule means that a vote on asylum to Snowden wouldn’t happen until 2016.
Snowden has been living in exile in Russia since June 2013 and faces US charges of espionage and theft of state property which could put him in jail for 30 years.
He says he was doing his duty as a citizen by informing others about the surveillance programmes which scooped up massive amounts of personal data in the name of national security.