Euro zone members have given Greece until the end of the week to come up with a proposal for sweeping reforms in return for loans that will keep the country from crashing out of Europe's currency bloc and into economic ruin.

"The stark reality is that we have only five days left ... Until now I have avoided talking about deadlines, but tonight I have to say loud and clear that the final deadline ends this week," European Council President Donald Tusk told a news conference.

Prime Minister Alexis Tsipras has until Friday to present the proposal, but German Chancellor Angela Merkel said she hoped to have convincing reform commitments from Tsipras on Thursday so she could ask the German parliament to authorize negotiations on a new aid program.

Merkel said she was "not exaggeratedly optimistic" for a solution.

At an emergency summit in Brussels on Tuesday, representatives of the 19-country euro zone said all 28 European Union leaders would meet on Sunday to decide Greece's fate. The talks were organised after Greeks voted in a referendum on Sunday against a bailout that carried stringent austerity measures.

French President Francois Hollande said the European Central Bank would ensure that Greek banks had the minimum necessary liquidity to stay afloat until Sunday.

The situation in Greece worsened with banks closed for a second week, limited cash withdrawals and businesses feeling the crunch of demands from vendors for cash payments.

Tsipras sounded upbeat as he left the summit, even though many of the reforms demanded by his partners would inflict more pain on Greeks who voted at his behest to reject the austerity measures in return for financial aid.

"The discussion took place in a positive climate," he said. "The process will be extremely fast. It starts in the coming hours, with the aim to conclude by the end of the week at the latest."

He promised to work for a socially just deal that would bring a "final exit" from the crisis, return Greece to growth and restructure Greek debt to make it viable.

Failure, Tusk warned, would undermine the EU's standing in the world and said the six-decade-old bloc may face "the most critical moment in our history".

Strict timetable laid out

Under a timetable agreed by the 19 leaders of the common currency area, Greece will submit on Wednesday a formal request for a two-year loan program, with a first list of reform commitments to be spelled out in greater detail on Thursday.

If the European Commission, the International Monetary Fund and the European Central Bank approve, Eurogroup finance ministers will meet on Saturday to recommend opening negotiations on a conditional assistance program.

"The ball is in Greece's court," Italian Prime Minister Matteo Renzi said, calling Sunday "the final meeting on Greece".

He said positions had hardened since previous bailout talks collapsed in late June, when Tsipras called a referendum at short notice to defy Greece's creditors.

Merkel said if Athens came up with satisfactory proposals and took "prior actions" by passing laws to convince creditors of its intent, short-term financing could be made available to help Greece over a repayment hump this summer.

She did not rule out rescheduling Greek debt in the longer run by extending loan maturities, lowering interest rates and allowing a longer moratorium on debt service payments, but she said a "haircut", or writedown, was impossible because it would be illegal.

Austrian Chancellor Werner Faymann warned that if there were no deal on Sunday, euro zone governments would have to prepare "Plan B," code for Greece losing all access to euros and finding itself excluded from the currency bloc.

Even EU chief executive Jean-Claude Juncker, who has worked tirelessly to keep Greece in the euro, said he now had detailed plans to cope with a "Grexit" if Tsipras failed to deliver.

People familiar with Greece's financial system said the banks could start running out of money within two days unless they received more liquidity.

Bridge financing

Euro zone sources said bridge financing could be provided by "Greece's friends" and by releasing past ECB profits on Greek bonds to prevent Athens from missing a crucial 3.5 billion euro bond redemption to the ECB due on July 20.

Some of Athens' 18 partners in Europe's common currency expressed exasperation at five years of crisis wrangling with Greece. Lithuanian President Dalia Grybauskaite complained, "With the Greek government it is every time manana."

Merkel, under pressure in Germany to cut Greece loose, made clear it was up to Tsipras to present convincing proposals after Athens spurned tax rises, spending cuts and pension and labor reforms that were on the table before its 240 billion euro (US$262.7 billion) bailout expired last week.

As of Tuesday night, she said, the conditions for opening new aid negotiations with Greece still had not been met.

Euro zone finance ministers complained that their new Greek colleague Euclid Tsakalotos, while more courteous than his abrasive predecessor Yanis Varoufakis, had brought no new proposals to a preparatory meeting before the summit.

"I have the strong impression there were 18 ... ministers of finance who felt the urgency of the situation and there is one ... who doesn't feel the urgency of the situation," Belgian Finance Minister Johan Van Overtveldt said.

Greek officials said the leftist government had broadly repeated a reform plan Tsipras sent to the euro zone last week.

Jeroen Dijsselbloem, chairman of the Eurogroup of currency zone finance ministers, said the ministers would hold a conference call on Wednesday to review a Greek request for a medium-term assistance program from the European Stability Mechanism bailout fund, due to be submitted within hours.

At stake is more than just the future of Greece, a nation of 11 million that makes up just two per cent of the euro zone's economic output and population.

If Greek banks run out of money and the country has to print its own currency, it could mean a state leaving the euro for the first time since it was launched in 1999, creating a precedent and fuelling doubts about the long-term viability of an incomplete European monetary union.

"Even if it did not trigger a short-term domino effect, the integrity of the euro zone would come under fresh threat with each episode of political uncertainty within member countries," said Thibault Mercier, an analyst at BNP Paribas.

Even in France, the euro zone country most sympathetic to Athens, an opinion poll published on Tuesday showed one in two people want Greece to leave the euro zone.