The head of the finance ministers, Jeroen Dijsselbloem of the Netherlands, said the agreement could “be implemented without delay” without a new vote by the Cypriot Parliament, which had rejected a deal last week. Lawmakers on Friday passed legislation that set the framework for the new action, he said.

“This has indeed been an arduous week for Cyprus,” he said.

He did not have exact timing for when Cyprus’s banks, which have been closed for more than a week, would reopen. Cyprus would receive the first payment of the bailout package worth 10 billion euros, or $13 billion, in early May.

Under the agreement, Laiki Bank, one of Cyprus’s largest, would be wound down and senior bondholders would take losses.

Depositors in the bank with accounts holding more than 100,000 euros would also be heavily penalized but the exact amount of those losses would need to be determined.

The plan to resolve Laiki Bank should allow the Bank of Cyprus, the country’s largest lender, to survive. But the Bank of Cyprus will take on some of Laiki’s liabilities in the form of emergency liquidity, which has been drip-fed to Laiki by the European Central Bank. That short-term financing, which the E.C.B. had threatened to cut off on Monday, is expected to continue.