ZADAR, Croatia — While Greece and Germany tussle over what debt forgiveness might mean, Croatia, the European Union’s newest member, is adopting its own approach, offering what it calls a “new beginning” to 60,000 of its poorest citizens.

Starting Monday, the government of Croatia, which joined the European Union in July 2013, offered a debt write-off to Croats who have blocked bank accounts, owe less than the equivalent of about $5,000 and currently receive some sort of welfare benefits. They also should have no property or savings beyond a primary residence.

By Wednesday, about 20,000 citizens had applied for the assistance, announced last month by Prime Minister Zoran Milanovic, who touted it as a unique scheme to help the poor as strapped European nations look for imaginative ways to clean up their finances but prevent further impoverishment.

“This is the first time that someone decided to solve this problem in this way,” Mr. Milanovic told Parliament. “Not by punishment or legal force, but through an agreement.”