* Cypriot bailout of 10 billion euros agreed by euro zone
* 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
The euro zone struck a deal 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 risks of a wider bank run.
Cyprus becomes the fifth country after Greece, Ireland, Portugal and Spain to turn to the euro zone for financial help in the wake of the region's debt crisis.
In a radical departure from previous aid packages, euro zone ministers forced Cyprus' savers, almost half of whom are believed to be non-resident Russians, to pay up to 10 percent of their deposits to raise almost 6 billion euros.
"I wish I was not the minister to do this," Cypriot Finance Minister Michael Sarris said after 10 hours of late-night talks where euro zone finance ministers agreed the package.
"Much more money could have been lost in a bankruptcy of the banking system or indeed of the country," he said, adding that he hoped a levy and bailout would mark a new start for Cyprus.
Without a rescue, Cyprus would default and threaten to unravel investor confidence in the euro zone that has been fostered by the European Central Bank's promise last year to do whatever it takes to shore up the currency bloc.
But on the Mediterranean island, initial incredulity at the decision gave way to anger.
Co-op credit societies, normally open on Saturdays, were shut for business in the coastal town of Larnaca as depositors started queuing early in the morning to withdraw their cash.
"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 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 levy on bank deposits will come into force on Tuesday, after a bank holiday on Monday. Cyprus will take immediate steps to prevent electronic money transfers over the weekend.
"As it is a contribution to the financial stability of Cyprus, it seems just to ask for a contribution of all deposit holders," Dutch Finance Minister Jeroen Dijsselbloem, who chaired the meeting in Brussels, told reporters.
Such levies break the taboo of hitting bank depositors with losses, but Dijsselbloem said it would not have otherwise been possible to salvage its financial sector, which is around eight times the size of the economy.
"We are not penalising Cyprus... we are dealing with the problems in Cyprus," Dijsselbloem said.
Dijsselbloem said that under the programme, the island's debt would fall to 100 percent of economic output by 2020.
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 Cypriot 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 meeting, said she backed the deal and would ask the IMF board in Washington to contribute to the bailout.
"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," Lagarde said.
Cyprus, with a gross domestic product of barely 0.2 percent of the bloc's overall output, applied for financial aid last June, but negotiations were stalled by the complexity of the deal and reluctance of the island's previous president to sign.
Moscow, which has close ties with Nicosia, is likely to help by extending a 2.5 billion euro loan already made to Cyprus by five years to 2021 and reducing the interest rate.
"We have had contacts in recent weeks with the Russian government," said the EU's top economic official Olli Rehn.
"My understanding is that the Russian government is ready to make a contribution with an extension of the loan and a reduction of the interest rate," said Rehn, who is responsible for economic affairs at the European Commission, the EU executive.
Cyprus' finance minister Sarris will travel to Moscow for meetings on Monday to try to pin down the new loan terms.
Cyprus originally estimated it needed about 17 billion euros - almost the size of its entire annual output - to restore its economy to health.
But because a loan of that magnitude would increase its debt to unsustainably high levels and call into question its ability ever to pay it back, policymakers sought to reduce it by finding more revenue sources in Cyprus itself.
Separately, euro zone ministers agreed to extend the maturity of emergency loans to Ireland and Portugal to smooth out their return to market financing this year and next, but details of the extensions will be decided only in April.