(REYKJAVIK) - More than 30,000 Icelanders -- almost one in eight potential voters -- had signed Wednesday a petition to demand a referendum on the pursuit of EU membership.

Thousands of protesters thronged the streets of Reykjavik Monday and Tuesday to demand a referendum after the government said it was dropping its EU membership bid without a popular vote.

The petition can be signed on a website (thjod.is) where the user needs to provide a Social Security number to guarantee a reliable count.

Iceland's eurosceptic government suspended EU accession talks indefinitely last September in line with an election pledge.

On Friday it announced a draft bill to "retract the application for membership of the European Union" which the island nation submitted in 2010.

Opposition parties complained that no time had been allocated for debate and the bill was postponed.

The government move is opposed by Icelanders from both the pro- and anti-EU side who accuse it of backtracking on a pledge to put the issue to the vote.

Iceland has been locked in conflict with the EU over fishing quotas and a majority of its voters oppose membership, but some argue that joining the bloc would stabilise the economy.

Recent polls indicate that a majority want the government to complete accession negotiations before putting membership to a referendum.

While the current EU bid would be dropped without a vote, under the government bill any new application would need a green light from a referendum before it can even begin -- setting up a further barrier to entry.

On Tuesday night, a heated debate in parliament highlighted deep divisions on the subject.

The leader of the Independence Party parliamentary group, Ragnheidur Rikhardsdottir, said she wanted to pursue accession talks to the end, and then let citizens decide.

The Left-Green Movement opposition party presented a bill to declare the negotiations suspended but not retracted.

New demonstrations were planned for Wednesday, after some 3,000 people gathered outside parliament Monday and Tuesday, the biggest protests since the country fell victim to the financial crisis in 2008-2009.