People in Cyprus have reacted with shock to news of a one-off levy of up to 10% on savings as part of a 10bn-euro (£8.7bn; $13bn) bailout agreed in Brussels.
Savers could be seen queuing at cash machines amid resentment at the charge.
The deal reached with euro partners and the IMF marks a radical departure from previous international aid packages.
President Nicos Anastasiades defended it as a "painful" step, taken to avoid a disorderly bankruptcy.
It had, he said in a statement, been a choice between the "catastrophic scenario of disorderly bankruptcy or the scenario of a painful but controlled management of the crisis".
The Cypriot leader, who was elected last month on a promise to tackle the country's debt crisis, will address the nation on Sunday.
Lenders are said to be gambling that the risk of a bigger banking crisis elsewhere in the eurozone has receded.
While Cyprus may be one of the eurozone's tiniest economies - its third-smallest - there could be serious repercussions for other financially over-stretched economies, such as those of Spain and Italy, BBC Business editor Robert Peston writes.
The point of the levy is to warn lenders to banks that they should take care where they place their funds, and avoid banks that overstretch themselves - as Cypriot banks did, he adds.
Cyprus is the fifth country after Greece, the Republic of Ireland, Portugal and Spain to turn to the eurozone for financial help during the region's debt crisis.
The country has been in financial difficulties since the collapse of the Greek economy, where Cypriot banks had huge investments.
It appears that the heavy presence of Russian money in Cypriot banks was a factor in imposing the levy.
People in Cyprus with less than 100,000 euros in their accounts will have to pay a one-time tax of 6.75%, Eurozone officials said.
Those with greater sums will lose 9.9%.
Depositors will be compensated with the equivalent amount in shares in their banks.
Reports suggest that depositors will be able to access all of their money except the amount set by the levy.
The levy itself will not take effect until Tuesday, following a public holiday, but action is being taken to control electronic money transfers over the weekend.
Co-operative banks, the only ones open in Cyprus on Saturday, closed after people started queuing to withdraw their money.
At one bank in the Limassol district, a frustrated man parked his bulldozer outside and threatened to break in.
Alan, a British expatriate saver in Cyprus, told BBC News: "This is robbery and we must get the EU to stop this.
"We retire and bring our savings to a bank in Cyprus and they can just take our money away without permission and then say we have shares in a bankrupt bank."
Maria Zembyla, from Nicosia, said the levy would make a "big dent" in her family's savings and "erode the investor confidence".
"Russians that currently keep the economy afloat will leave the country along with their money," she added.
According to Reuters news agency, almost half of the depositors in Cyprus are believed to be non-resident Russians.
There has also been speculation that Russia could help finance the bailout by extending a 2.5bn-euro loan already made to Cyprus.
Cyprus Finance Minister Michael Sarris will travel to Moscow for meetings on Monday, reports say.
"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 the EU's top economic official, Olli Rehn.
European regulators and politicians are convinced that a vast amount of cash in Cypriot banks belongs to Russian money launderers, our business editor writes.
Few German politicians would vote for a Cyprus rescue that simultaneously rescued these launderers so the only way to make the bailout palatable to the German parliament was to tax the launderers, too, he says.
Russians reacted angrily to the news of the levy on social media.
"Russia agrees to help a troubled EU state, and the EU calls Russian investors money-launderers? This is totally unfair," Moscow-based blogger Igor Kim told the BBC News website.
"Levying a 10% charge on investors is barbarian, interventionist and more Soviet than the Soviet Union!"
In Berlin, German Finance Minister Wolfgang Schaeuble called the levy part of the "fair" distribution of the bailout's burden.
"Profit expectations and risk have to coincide again, this gap [between the two] was one of the grave mistakes of the financial bailout [in 2008], and we have learned the lesson," he said.