* Euro zone finance ministers agree 10-billion-euro rescue
* One-off levy on bank deposits to raise almost 6 bln euros
* IMF's Lagarde says backs deal, will make contribution soon
* Cypriots' incredulity at decision gives way to fury
* Spain government source denies same levy possible elsewhere
By Annika Breidthardt and Robin Emmott and Michele Kambas
BRUSSELS/NICOSIA, March 16 (Reuters) - The euro zone agreed on Saturday to hand Cyprus a bailout worth 10 billion euros ($13 billion), but demanded depositors in its banks forfeit some money to stave off bankruptcy despite the risk of a wider run on savings.
The eastern Mediterranean island becomes the fifth country after Greece, Ireland, Portugal and Spain to turn to the euro zone for financial help during the region's debt crisis.
In a radical departure from previous aid packages - and one that gave rise to incredulity and anger across the country - euro zone finance ministers forced Cyprus' savers to pay up to 10 percent of their deposits to raise almost 6 billion euros.
Parliament was due to meet on Sunday to vote on the measure, and approval was far from assured.
The decision prompted a run on cashpoints, most of which were depleted by mid afternoon, and co-operative credit societies closed to prevent angry savers withdrawing deposits.
Almost half Cyprus's bank depositors are believed to be non-resident Russians, but most queuing on Saturday at automatic teller machines appeared to be Cypriots..
President Nicos Anastasiades, elected three weeks ago with a pledge to negotiate a swift bailout, said refusal to agree to terms would have led to the collapse of the two largest banks.
"On Tuesday ... We would either choose the catastrophic scenario of disorderly bankruptcy or the scenario of a painful but controlled management of the crisis," Anastasiades said in written statement.
In several statements since his election, he had previously categorically ruled out a deposit haircut.
"My initial reaction is one of shock," said Nicholas Papadopoulos, head of parliament's financial affairs committee. "This decision is much worse than what we expected and contrary to what the government was assuring us, right up until last night," he told Reuters, without saying whether he would back the measure or whether he thought it would pass.
Papadopoulos is vice-chairman of the Democratic Party, a partner in Cyprus's centre-right ruling coalition and whose support in parliament will be crucial to pass any haircut.
Parliament was expected to convene from 1600 local (1400 GMT) on Sunday to discuss the emergency legislation. Without parliamentary approval, a haircut cannot take place.
The bailout was smaller than initially expected and is mainly needed to recapitalise Cypriot banks that were hit by a sovereign debt restructuring in Greece.
The deposit levy - set at 9.9 percent on bank deposits exceeding 100,000 euros and 6.7 percent on anything below that - will take place on Tuesday after a bank holiday on Monday.
To guard against capital flight, Cyprus took immediate steps to prevent electronic money transfers over the weekend.
At one cashpoint in the capital Nicosia, a pensioner couple said they had visited several automatic teller machines without success. "We are trying to pull as much as we can," one told Reuters, reaching for a wallet containing four debit cards.
"I'm extremely angry. I worked years and years to get it together and now I am losing it on the say-so of the Dutch and the Germans," said British-Cypriot Andy Georgiou, 54, who returned to Cyprus in mid-2012 with his savings.
"They call Sicily the island of the mafia. It's not Sicily, it's Cyprus. This is theft, pure and simple," said a pensioner.
The levy breaks a euro zone taboo by hitting depositors.
It prompted Spain, considered the next most likely state to seek a sovereign rescue though supported recently by a European Central Bank promise to buy government debt if necessary, to deny savers in other countries risked being similarly penalised.
The bailout was specific to Cyprus and its bloated banking sector and "could not be extrapolated to any other country," an economy ministry source in Madrid said.
In Brussels, Dutch Finance Minister Jeroen Dijsselbloem said it would not otherwise have been possible to save Cyprus's financial sector which, compared with national economic output, is more than twice as big as the EU average.
"As it is a contribution to the financial stability of Cyprus, it seems just to ask for a contribution of all deposit holders," Dijsselbloem, who chaired the ministerial meeting, told reporters.
The island's bailout had repeatedly been delayed amid concerns from other EU states that its close business relations with Russia, and a banking system flush with Russian cash, made it a conduit for money-laundering.
In return for emergency loans, Cyprus agreed to increase its corporate tax rate by 2.5 percentage points to 12.5 percent. This should boost revenues, limiting the size of the loan needed from the euro zone and keep down public debt.
International Monetary Fund Managing Director Christine Lagarde, who attended the Brussels meeting, said she backed the deal and would ask the IMF board in Washington to contribute.
"We believe the proposal is sustainable for the Cyprus economy," she said. "The IMF is considering proposing a contribution to the financing of the package ... The exact amount is not yet specified."
Cyprus, with a gross domestic product of barely 0.2 percent of the bloc's overall output, applied for aid last June. But negotiations became bogged down.
Moscow, with close ties to Nicosia, will also likely extend a 2.5 billion euro loan by five years to 2021 at a lower cost.
"My understanding is that the Russian government is ready to make (such) a contribution," said the EU's top economic official, Olli Rehn.
Cyprus originally estimated it needed 17 billion euros - almost its annual output - to restore its economy to health.
But because a loan of that magnitude would call into question its ability ever to pay it back, policymakers sought more revenue sources in Cyprus itself.
The Greek units of Cypriot banks were excluded from the deposit levy, Greek finance minister Yiannis Stournaras said.