The eurozone has given Greece until Thursday to present new proposals to secure a deal with creditors, and has called a full EU summit for Sunday.
European Council President Donald Tusk said this was now the "most critical moment in the history of the eurozone".
"The final deadline ends this week," he said after emergency talks in Brussels.
The eurozone had expected Greece to submit fresh plans on Tuesday after its voters rejected a deal in a referendum, but no new proposals were tabled.
On Sunday, a meeting of all 28 members of the EU will be held - a day after the new Greek proposals are expected to be discussed by the eurozone finance ministers.
In Brussels, Greece has been given an ultimatum: either there will be a deal or Greece and its banks face the prospect of going bust on Monday, the BBC's Chris Morris in the Belgian capital reports.
'Fast process'
Speaking at a news conference late on Tuesday, Mr Tusk said a Greek bankruptcy and the collapse of the Greek banking system would affect the whole of Europe, and that anyone who thought otherwise was naive.
French President Francois Hollande said: "It's not just the problem of Greece - it's the future of the European Union" that is at stake.
Meanwhile, Greek Prime Minister Alexis Tsipras said he wanted a "socially just and economically viable agreement".
"The process will be fast. It starts in the coming hours with the aim of concluding it by the end of the week, at the latest," he said.
Mr Tsipras is due to address the European parliament in Strasbourg later on Wednesday.
What are the scenarios for Greece?
Source: BBC