BRUSSELS — Struggling into the early-morning hours to avoid a collapse of Cyprus’s banking system, European Union leaders on Monday agreed on a bailout package intended to keep Cyprus in the euro zone and rebuild its devastated economy.

The deal, struck after hours of meetings here, was approved by the finance ministers from the euro zone, the 17 countries that use the common currency. It would drastically prune the size of Cyprus’s oversize banking sector, bloated by billions of dollars from Russia and elsewhere in the former Soviet Union.  Read more