Jeroen Dijsselbloem, chairman of the 19-nation Eurogroup, told a news conference: "We will work very hard in the next few days, the institutions with the Greek government, to get that deal this week."
The ministers agreed to reconvene later this week, after Greece has thrashed out details with its international creditors - the European Commission, the European Central Bank (ECB) and the International Monetary Fund (IMF).
Dijsselbloem described the Greek document as comprehensive and "a basis to really restart the talks" but said it remained to be seen whether the numbers added up to make Athens' public finances sustainable.
Heads of state and government of the euro zone were to hold an emergency summit on the crisis on Monday evening but officials made clear in advance that they would not negotiate on details of the program, only agree on a political timetable for a deal. They dismissed a rumour in German media that the summit had been cancelled.
Asked for his assessment of the Greek proposals, transmitted to Brussels early on Monday, EU Economics Commissioner Pierre Moscovici said: "It's a solid, and at last global, basis (for negotiations), but there is more work to be done."
Athens has to make a euro 1.6-billion repayment to the IMF by June 30 or be declared in default, potentially triggering capital controls to stem a bank run and pushing Greece closer to the exit from the euro zone.
With anxious savers already withdrawing cash en masse, fearing emergency controls, the European Central Bank increased its emergency liquidity assistance to Greek lenders for the third time in a week.
But after months of acrimony between Greece and its creditors, the positive mood music in Brussels injected new hope that an agreement might be near.
Shares surge
European shares surged and the Greek stock market .ATG jumped 8 per cent while the borrowing costs of Italy, Spain and Portugal - the countries most likely to be hit if Greece headed for the euro zone exit - fell sharply.
In the proposal sent early on Monday, Greece moved to acquiesce to lenders' demands for tax increases and pension reform by offering to raise the retirement age gradually to 67 and curb early retirement. It also offered to reform the value-added-tax system to set the main rate at 23 per cent.
Chancellor Angela Merkel of Germany, the biggest European contributor to Greece's bailout programmes, held open the possibility of a deal. "There are still a lot of days in the week in which decisions can be taken," she told reporters in Magdeburg.
But German Finance Minister Wolfgang Schaeuble, who has taken a consistently hard line with Athens, was pessimistic.
"There is nothing new beyond many trying to create expectations which are not supported by substance," he said. "Without substantial proposals which can be examined seriously, we can't seriously prepare a euro summit."
In a sign of the angry mood among Merkel's conservatives toward Greece, former German interior minister Hans-Peter Friedrich said there was no point in "dragging out a bankruptcy for political reasons".
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