The most contentious issue in months of negotiations was whether to force Cypriot depositors to take losses in order to make the country’s debt more manageable. The Cypriot authorities had sought to head off any such initiatives on the grounds that they would do lasting damage to their financial services sector.
In the early hours of Saturday morning, after 10 hours of talks, finance ministers from euro area countries, the International Monetary Fund and the European Central Bank agreed on terms that include a one-time tax of 9.9 percent on Cypriot bank deposits of more than $130,000, or 100,000 euros, and a tax of 6.75 percent on smaller deposits, European Union officials said.
“It’s not a pleasant outcome especially for the people involved,” Michalis Sarris, the Cypriot finance minister, told reporters. “But we believe it is something that, compared with other possible outcomes, is the least onerous,” he said.
“This is a once and for all levy,” Mr. Sarris added, saying it should ensure no further flight of depositors from Cypriot banks. The measure should “remove any doubt about the future” for Cypriot depositors, he said.
Cypriot authorities had begun to monitor deposit outflows from Cypriot lenders to watch for signs of a bank run ahead of Tuesday when the levy is expected to be imposed, E.U. officials said.
Jeroen Dijsselbloem, the president of the group of euro area ministers, told a separate news conference that lenders had reached “a political agreement” to aid Cyprus. The challenges to reaching a deal were “of an exceptional nature,” he said.
The latest bailout for the euro zone broke new ground by requiring haircuts, or losses for all Cypriot bank depositors. A previous bailout for Greece required a significant haircut for holders of Greek bonds in early 2012 – something that European Union officials said at the time would be a one-of-a-kind measure.
Mr. Dijsselbloem declined to rule out taxes on depositors in other countries besides Cyprus in the future, but he insisted that such a measure was not being considered.
Going into the meeting, finance ministers sought to limit the overall costs of the rescue plan while Christine Lagarde, the managing director of the I.M.F., pushed for a deal that is generous enough to enable Cyprus eventually to pay the money back.
The Cypriot authorities wanted a plan that ensures that the island remains attractive to investors, who include many Russians with large deposits in the country’s banks.
Under the deal, depositors would be compensated with shares in the banks, giving some “upside potential” to the measure, Mr. Sarris said.
Ahead of the meeting, Ms. Lagarde was blunt about the need for ministers to agree to a realistic package of measures. “All I know is that we don’t want a Band-Aid,” she said. “We want something that lasts, something that is durable and that will be sustainable.”
Ms. Lagarde told the news conference after the meeting that she would recommend that the I.M.F. make a contribution to the package for Cyprus. She said the size of that contribution still needed to be determined.
The key to a breakthrough was finding a way to bring down the bailout package, originally estimated at 17 billion euros ($22.2 billion), which represents almost as much as Cyprus’s gross domestic product, which is about $23 billion, or 18 billion euros.
The deal that emerged on Saturday morning was for a bailout of up to 10 billion euros, Mr. Dijsselbloem said.
Cyprus asked for the bailout in June last year. But talks faltered when the former president Demetris Christofias, a Communist, balked at measures like privatizations. The talks sped up after the election last month of Nicos Anastasiades of the Democratic Rally, a center-right party, to the presidency.
Some of the other elements of the deal involved Cyprus raising its low corporate tax rate to 12.5 percent from 10 percent, privatizing state assets and overhauling its banks to ensure that they are not havens for money laundering.
Russia also was expected to contribute to the arrangement, perhaps by agreeing to lower the interest rate on a loan worth 2.5 billion euros it has already made to Cyprus.