– Greece took a step back from the abyss on Monday with the presentation of new budget proposals that eurozone leaders welcomed as a basis for a possible agreement in the coming days to unlock frozen aid and avert a looming default.

European Council President Donald Tusk, who chaired an emergency summit of leaders of the 19-nation currency bloc, called the Greek proposals "a positive step forward." He said the aim was to have the Eurogroup finance ministers approve a cash-for-reform package on Wednesday evening and put it to eurozone leaders for final endorsement on Thursday morning.

However, there must first be a detailed agreement with representatives of European governments, the European Central Bank and the International Monetary Fund to ensure the numbers add up, he said.

European stock markets and Greek assets surged on Monday on hopes of a last-minute deal to ease a crisis that is threatening to drive Greece out of the euro and weaken the foundations of the European Union's single currency.

"I am convinced that we will come to a final agreement in the course of this week," European Commission President Jean-Claude Juncker told a late-night news conference.

German Chancellor Angela Merkel, whose country is Greece's biggest creditor, was more cautious. "I can't give any guarantee that that will happen," she said of a final agreement. "There's still a lot of work to be done."

The Greek proposals included higher taxes and welfare charges and steps to curtail early retirement, but not the nominal pension and wage cuts first sought by lenders. Leftist Prime Minister Alexis Tsipras, elected in January on a promise to end austerity measures, also appeared to have avoided raising value added tax on electricity or loosening job protection laws.

The cash-starved country must repay the IMF 1.6 billion euros by June 30 or be declared in default, potentially triggering a bank run and capital controls.

Jeroen Dijsselbloem, chairman of the eurozone finance ministers, described the new Greek document as comprehensive and "a basis to really restart the talks." He said negotiations in the coming days would show whether the numbers added up.

He left the summit saying only that there would be "hard work for the next few hours."

German Finance Minister Wolfgang Schaeuble was the most negative, telling reporters earlier in the day he had seen nothing really new from Greece.

Participants said Schaeuble questioned in the Eurogroup meeting whether the European Central Bank should continue emergency lending to Greek banks if there was no deal this week and whether it should not be accompanied by capital controls.

A Greek official said ECB chief Mario Draghi had reassured Tsipras in a private meeting that the central bank would continue to support Greek banks as long as Athens remained in a bailout program.

Participants said IMF chief Christine Lagarde cast doubt in the meeting on whether the proposals were sufficient to make Greece's public finances sustainable.

"We have a huge amount of work to do in the next 48 hours. We are not at all at the end of the route," Lagarde said on leaving the summit.