EU leaders say Greece has agreed to come up with a new reform plan within days to secure the additional bailout funds required to prevent bankruptcy.
The development came after marathon talks between Greek PM Alexis Tsipras, German Chancellor Angela Merkel and other European leaders in Brussels.
Mr Tsipras said he was now "more optimistic" after the meeting.
Separately, the EU leaders agreed to keep sanctions on Russia in place until the end of this year at the earliest.
The sanctions, imposed because of Russia's alleged military intervention in Ukraine, are now linked to "complete implementation" of a ceasefire deal.
The middle-of-the-night talks between Mr Tsipras, Ms Merkel, French President Francois Hollande and leaders of the EU institutions lasted for more than three hours. They were organised on the sidelines of an EU summit in the Belgian capital.
Speaking afterwards, Ms Merkel said: "The Greek government will take full responsibility for the reforms and submit a list of these reforms... in the coming days."
Describing the meeting as "good and constructive", she warned that "everything is supposed to be completed quickly and everyone needs to do his or her bit".
Mr Tsipras said: "I'm more optimistic after this deliberation. I think that all the sides confirmed their intention to try to do their best to overcome the difficulties of the Greek economy as soon as possible."
The BBC's Damian Grammaticus in Brussels reports a senior EU official as saying that the message to Greece was simple - "give us a list fast, then you can get the money fast".
But our correspondent adds that only once that list of reforms is evaluated for its impact on Greece's finances - and approved - will the other nations that use the euro hand over more money.
The current assumption is that Greece has only enough cash to meet all its obligations until sometime next month.
International creditors have suggested they are ready to extend help on Greece's €240bn (£176bn; $272bn) bailout until the end of June.
But Mr Tsipras's earlier reform plans had met resistance from EU leaders, with Germany among the most critical.