BRUSSELS--The euro zone must complete a bailout deal for Cyprus Sunday night in order to safeguard the stability of the euro zone, Luxembourg Finance Minister Luc Frieden said Sunday.

"It is about much more than cyprus, it is about the stability in the euro zone and therefore we must find a solution together," he said. "Finding a solution here is very difficult, the situation is very serious. But we need a solution tonight because it's about the instability of the whole euro zone, and endangering that would be very bad."

He said a bailout deal for Cyprus is a question not only of helping Cyprus but "a question of helping ourselves."

Mr. Frieden said the Cypriot banking sector is clearly going to be considerably changed in the aftermath of the bailout deal, but he said it is important as many Cypriot banks survive as possible.

Cypriot authorities have passed a law to allow them to step in and resolve the Cyprus Popular Bank, and they are expected to protect insured deposits of up to 100,000 euros ($130,000). A decision must still be made on the future of Bank of Cyprus.

-Write to Tom Fairless and Laurence Norman at Tom.Fairless@dowjones.com and Laurence.norman@dowjones.com