ATHENS — Greece and its international creditors said on Tuesday that they had reached agreement on the country’s next round of economic changes, a deal that is meant to unlock as much as 12 billion euros, or about $13 billion, in loan money.

Athens had initially hoped the money would be dispensed after the Greek Parliament passed a package of economic measures last month.

But eurozone finance ministers said then that the steps did not fully meet the conditions required for the next milestone payment from the country’s €86 billion bailout package.

The breakthrough this time was a formula for providing some overly indebted homeowners protection from foreclosure, even as Greece and the creditors try to protect Greek banks from the worst effects of borrowers who cannot repay their loans.