BRUSSELS — European leaders gathering here on Thursday for their year-end summit meeting hailed an agreement to place euro zone banks under a single supervisor, calling it a concrete measure to maintain the viability of the currency as well as a step in laying the groundwork for a broader economic union.

The agreement was reached during an all-night negotiating session of finance ministers that ended early Thursday after France and Germany made significant compromises. Under the agreement, 100 to 200 large banks in the euro zone will fall under the direct supervision of the European Central Bank.

A round of talks a week earlier broke up because of French and German discord over how many banks in the currency union should be covered by the new system.

In a concession to Germany, the finance ministers agreed that thousands of smaller banks would be primarily overseen by national regulators. But to satisfy the French, who wanted all euro zone banks to be held accountable, the central bank will be able to take over supervision of any bank in the region at any time.