Greek Prime Minister Alexis Tsipras won a commitment to seek a last-minute rescue at an emergency euro zone summit on Tuesday, before his country's banks run out of money.
Italian Prime Minister Matteo Renzi told reporters that EU leaders would hold a further summit on Sunday to approve a plan to aid Greece if creditor institutions are satisfied in the meantime with a Greek loan application and reform commitments.
"The ball is in Greece's court," Renzi said. "Next Sunday the final meeting will take place on Greece."
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German Chancellor Angela Merkel, who arrived in Brussels saying there was still no basis for reopening negotiations with Athens, changed her tune in the room and was actively involved in efforts to find a last-ditch solution, euro zone sources said.
"It is not a matter of weeks but of a few days" to save Greece from collapse, Merkel told reporters on arrival.
With Greek banks down to their last few days of cash and the European Central Bank tightening the noose on their funding, Tsipras tried to convince the euro zone's other 18 leaders to authorize a new loan swiftly.
People familiar with Greece's financial system said the banks could start running out of money within two days unless there was an international rescue.
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However, euro zone sources in Brussels said ECB President Mario Draghi had assured finance ministers that the central bank would keep Greek lenders afloat this week as long as negotiations were under way.
Merkel and French President Francois Hollande worked together on a plan to save Greecefrom plunging into economic turmoil and possibly having to ditch the euro. This involved a medium-term conditional program and a short-term interim financing deal for a few months, the sources said.
However, a solution still depends on Tsipras putting forward convincing reform proposals and rushing key measures through parliament by the weekend to make Greece's public finances sustainable.
If he does, 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 on July 20, the sources said.
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Some of Athens' 18 partners in Europe's common currency vented 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 ($262.7 billion) bailout expired last week.
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.
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"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 broadly repeated a reform plan Tsipras sent to the euro zone last week before Greek voters, in a referendum on Sunday, overwhelmingly rejected the austerity terms previously on offer for a bailout.
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.
Tsipras met privately with the leaders of Germany and France, the currency area's main powers, and European Commission president Jean-Claude Juncker just before the summit began.
(Additional reporting by Costas Pitas, Angeliki Koutantou and George Georgiopoulos in Athens, Julia Fioretti and Alastair Macdonald in Brussels, Paul Carrel in Berlin John O'Donnell in Frankfurt and Mark John in Paris; Writing by Paul Taylor; Editing by Mark Trevelyan)