The eurozone has told debt-hit Cyprus to revise a controversial levy on bank deposits to allow small savers to escape the tax, part of a larger bailout deal, amid a public outcry and fears of a bank run. The statement from eurozone finance ministers came Monday after Cyprus baulked at putting the bailout plans to a parliamentary vote, as the growing uncertainty forced a prolonged closure of the island's banks. Cyprus shut its banks until at least Thursday and delayed a parliamentary vote on the package until Tuesday after large queues formed at ATMs on the island. The planned levy on bank savings was agreed on Saturday by the eurozone partners in exchange for a 10-billion-euro ($13 billion) sovereign bailout deal for debt-laden Cyprus. On Monday the finance ministers stressed that "small depositors should be treated differently from large depositors" and the importance of fully guaranteeing bank deposits below 100,000 euros, Eurogroup President Jeroen Dijsselbloem of The Netherlands said in the release. The hastily-convened ministerial talks saw Dijsselbloem "reiterate that the stability levy on deposits is a one-off measure," seeking to reassure savers elsewhere in the eurozone. The move came as analysts suggested the European Union had shot itself in the foot with the bank levy decision and media lampooned "the Great Euro Bank Robbery". In the original bailout accord agreed early Saturday with the EU, the IMF and the ECB, Cyprus agreed to impose a levy of 6.75 percent on bank accounts up to 100,000 euros ($129,000) and 9.9 percent for larger deposits. The one-time move was aimed at raising 5.8 billion euros for the government. The Eurogroup statement said that emergency re-negotiations would see Nicosia "introduce more progressivity in the one-off levy", in other words increasing the tax rate on bigger holdings to ensure the same 5.8-billion-euro return. A eurozone source spelled out that this would mean preferably removing altogether the mooted 6.75-percent levy applied to smaller accounts, which combined amount to more than three fifths of all Cypriot savings, despite some 30 billion euros attributed to large Russian investors. The head of the European bailout fund, Klaus Regling, warned the Cypriot government against changing the underlying terms of the bailout plan. In an interview in Tuesday's edition of the Germany Bild daily, the director of the 500-billion-euro European Stability Mechanism (ESM) said that while the question of how the contributions from Cyprus were levied was a matter for the government there. However "there must be a contribution from Cyprus equivalent to the sum decided" with its eurozone partners. He added that an uncontrolled default, even of such a relatively small economy, would threaten the euro. The economic and political fallout was huge following the announcement that a raid on savings would be required as part of the fifth eurozone bailout of the three-year debt crisis. Moscow, which has an outstanding 2.5 billion euro loan to Cyprus and billions more in deposits in the island's banks, reacted angrily to the EU levy. Russian President Vladimir Putin slammed the "dangerous" move and turmoil hit stock and currency trades on Monday amid concerns that a precedent had been set for bigger debt-saddled eurozone economies such as Italy and Spain. Estimates vary but the Moody's rating firm estimates that Russian companies and banks keep up to $31 billion in Cyprus, which accounts for between a third and half of all Cypriot deposits. Cypriot Finance Minister Michalis Sarris is due in Moscow on Wednesday for what looked certain to be awkward talks -- a day before the head of the European Commission, a member of the bailout "troika," also lands in Moscow to meet Prime Minister Dmitry Medvedev. After markets suffered losses on Monday, Asian bourses rebounded early Tuesday as news spread that Cyprus was reworking the controversial savings levy. Tokyo stocks led the way, finishing morning trading 2.02 percent higher. The euro also rebounded in Asia, fetching $1.2961, up from $1.2957 in New York on Monday. In coming up with the bailout deal, eurozone leaders rejected a Cypriot request for 17 billion euros in rescue financing, insisting such a large debt would be unsustainable for the Mediterranean holiday island of less than one million people. They offered instead 10 billion euros, insisting the balance be made up from within the island, principally through the levy on bank deposits. Hundreds of protesters gathered outside the parliament building in Nicosia on Monday to register their anger at the unprecedented tax, not asked of other eurozone countries that have sought rescue. "Wake up, they are sucking our blood," demonstrators called to their fellow Cypriots. "If European policymakers were looking for a way to undermine the public trust that underpins the foundation of any banking system, they could not have done a better job," said CMC Markets analyst Michael Hewson. The Cyprus stock market said it too would remain closed if the banks did. Washington called for a "responsible and fair" resolution of the crisis.