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.