Eurozone finance ministers have broken off talks without an agreement on Greece's bailout.
But the officials say they aim to reach a deal later this week that might keep the country from defaulting and falling out of the currency union.
The lack of a result leaves a summit of government leaders later in the day with few prospects of making any concrete decisions on the country's crisis.
Greece needs more loans from its creditors, which include its fellow eurozone states and the International Monetary Fund, in time for June 30, when it faces a debt repayment it cannot afford.
The country has been negotiating for four months what economic reforms it should make to get the money.
Ahead of the meetings in Brussels, German Chancellor Angela Merkel and other European officials had warned against expecting too much on Monday.
Markets had rallied strongly in the morning on hopes that new proposals for reforms submitted by the Greek government over the weekend would pave the way for a deal. Those gains faded somewhat as it became clear that a deal would have to wait a little longer yet.
European Union leaders have a two-day summit starting on Thursday and hopes are a full agreement can be reached then.
Jeroen Dijsselbloem, the Dutchman who heads the eurozone finance minister meetings, said negotiators would be using proposals made this weekend by Greek Prime Minister Alexis Tsipras as a basis for further talks. "It's an opportunity to get that deal this week," he said.
European Commission President Jean-Claude Juncker said Greece's new proposals were a sign of progress but warned that "we are not yet there".
No details of the proposals were made public.
Despite the upbeat mood in markets, tension was palpable in Greece, where people flocked to cash machines to withdraw money. The concern is that a debt default by Greece could destabilise the country enough that it might have to eventually leave the euro.
To support Greek banks in the face of growing money withdrawals, the European Central Bank increased Monday the amount of emergency credit it allows the banks to draw on, a banking official said.
An exit from the euro would be hugely painful for Greeks, plunging the country back into a deep and long recession.
Experts are more divided about its effects on Europe and the world economy. Some say it would be manageable, but others note there is huge uncertainty. Several European countries have said publicly they are getting prepared for such an eventuality.
Greece has a debt repayment on June 30 worth 1.6 billion euro (£1.1bn) that it cannot afford without more loans. The talks are currently about releasing the last 7.2 billion euro (£5.2bn) in the country's bailout programme, which expires at the end of the month.
Since coming to power in January, the new government has refused to make more budget austerity measures, which it blames for devastating the economy.
It has since softened its approach, but it remains reluctant to take the steps creditors demand.
Over the past weeks, the creditors have often complained that Greek proposals on what kind of reforms they would implement have been too slow to come and far too vague.
German Finance Minister Wolfgang Schaeuble said that despite the new Greek plan, "we have so far received no substantive proposals".