This article has been updated.
BRUSSELS -- Frustrated and angered eurozone leaders gave Greek Prime Minister Alexis Tsipras a last-minute chance Tuesday to finally come up with a viable proposal on how to save his country from financial ruin.
Overcoming their surprise when Tsipras failed to present them with a detailed plan, the leaders reluctantly agreed to a final summit Sunday, saying that could give both sides an opportunity to stave off collapse of the struggling but defiant member nation.
With Greece's banks just days away from a potential collapse that could drag the country out of the euro, Tsipras arrived with only vague proposals and a commitment to back it up with real figures and a more detailed plan by Thursday.
"We'll see if on Sunday this issue will be solved once for all," Italian Prime Minister Matteo Renzi said.
But patience among Greece's allies was wearing very thin ahead of the meeting.
WATCH: A deal in Greece to come this week?
"You know, there was a promise for today. Then, they're promising for tomorrow," said Lithuanian President Dalia Grybauskaite. "For the Greek government it's every time 'manana.'"
Tsipras came buoyed by a triumph in last Sunday's referendum, where an overwhelming majority of Greeks backed his call to reject the belt-tightening reforms that creditors had last proposed.
But that domestic victory did not appear to give him much leverage in talks with foreign creditors, who know Tsipras needs a deal soon to keep his country afloat. Banks have been shut since last week and will not reopen before Thursday, cash withdrawals have been limited for just as long, and daily business throughout the country has come to a near standstill.
So it was with astonishment and dismay that European leaders learned Tsipras did not yet have a written proposal for new rescue aid.
"I'm extremely somber about this summit. I'm also somber about the question of whether Greece really wants to come up with proposals, with a solution," Dutch Prime Minister Mark Rutte said.
Greece's eurozone partners have steadfastly said they want to help Greece stay in the currency club but have just as often complained about Greece dragging its feet during months of negotiations.
WATCH: Where does Greece go from here?
"At a certain point, you need to get to the truth," said Belgian Prime Minister Charles Michel, before asking: "Is there, yes or no, a political will of the Greek government?"
A Greek government official said Tsipras was presenting a "common ground" to the 18 other leaders Tuesday, while a detailed proposal would come Wednesday.
He said the Greek government would submit a request for immediate financing in advance of 5 billion euros in loans due for repayment by the end of the month. He predicted a full political deal could be reached in two or three weeks.
German Chancellor Angela Merkel warned Tsipras he was dancing close to the financial abyss.
"We are no longer talking about weeks but very few days," she said.
In his flurry of contacts, Tsipras spoke by phone with President Barack Obama, and the White House said it was in Europe's interest to reach a resolution that puts Greece on the path toward economic growth and stability.
Normal commerce is now impossible in Greece. Small businesses, lacking use of credit cards or money from bank accounts, were left to rely on cash from diminishing purchases from customers, as Greeks hold on tight to what they have. And suppliers are demanding that businesses pay cash up front.
Giorgos Kafkaris, a 77-year-old pensioner, was among Greeks standing in line to withdraw cash at an Athens ATM on Tuesday.
"I came to get the 120 euros, I can't take more. The good thing is we had sorted things out earlier and we had 200-300 euros set aside," he said. "I'm waiting for something better for all of us. I believe something better will happen."
Greece has been granted two bailout programs worth a total of 240 billion euros ($266 billion) in loans from other eurozone countries and the International Monetary Fund.
But the spending cuts and tax increases demanded as a condition for the loans have hit growth, sending the country into a six-year recession and pushing unemployment to 25 percent. The government, meanwhile, has been slower than hoped in making the economy more competitive and selling state assets to raise money.