BRUSSELS — Cyprus reached a long-awaited bailout agreement early Saturday worth $13 billion, or 10 billion euros, that puts some of the burden for shoring up the island’s beleaguered economy on its bank depositors.

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.