Greece could descend into "chaos" unless a deal is found soon, the head of the French central bank Christian Noyer said on Wednesday.
"The Greek economy is on the edge of catastrophe. A deal absolutely must be [made] on Sunday because it will be too late after that and the consequences will be serious," he told French radio, adding that "there could be riots... and chaos in the country".
Noyer said it was "impossible" to re-open Greek banks while confidence was so low, saying there would be an "immediate run" on tellers.
The head of the French central bank is a member of the European Central Bank (ECB)'s decision-making governing council.
Noyer's warning came a day after European leaders held an emergency summit in Brussels to try to thrash out a deal to stop Greece crashing out of the euro.
Noyer said Greece’s ECB lifeline, which has stretched to €89 billion in recent months, could not be carried on indefinitely.
"We have rules and we have interpreted the rules to their limit to maintain a lifeline to Greek banks, but we cannot continue indefinitely to increase the risks we are taking," he said.
However, the summit failed to resolve differences and another one has been tabled for Sunday.
Greece's government must offer a new package of reform proposals by Thursday in advance of a meeting of eurozone finance ministers on Saturday and the full leaders' summit on Sunday.
Speaking after the summit, French president François Hollande said Greece still needs to make "credible and serious proposals" that prove it wants to remain part of the 19-nation eurozone.
The French leader spoke to reporters late on Tuesday after an inconclusive summit meeting of eurozone nations.
Respecting the rules, Hollande said, "is a condition of living together."
"What's at stake is to know the place of Greece in the European Union and thus the eurozone," Hollande said. "Today, there is no more time to waste."
The eurozone had expected Greece's newly appointed finance minister, Euclid Tsakalotos, to submit new reform plans on Tuesday after Greeks voted in a referendum Sunday to reject creditor demands for more austerity in return for fresh EU-IMF bailout funds.
When the proposals were pushed further into the week, European Commission President Jean-Claude Juncker warned "we have a 'Grexit' scenario prepared in detail" if no deal is reached, although he insisted he wanted Athens to stay
in the single currency.
German Chancellor Angela Merkel, meanwhile, warned Greece would need a debt programme lasting "several years" to revive its moribund economy and insisted writing off any part of its 320-billion-euro ($350-billion) debt mountain was
out of the question.
The EU's economic affairs commissioner Pierre Moscovici said an agreement with Greece was possible, but that it was up to its government to make credible proposals to its fellow eurozone members.
"I think a solution must be found by Sunday and I believe it can be," he told France 2 TV, adding: "The ball is clearly in the Greek authorities' court."