The International Monetary Fund has dramatically raised the stakes in Greece’s stalled debt talks, announcing that its delegation had broken off negotiations in Brussels and flown home because of major differences with Athens.

The surprise IMF announcement came as the European Union told leftist Greek Prime Minister Alexis Tsipras bluntly to stop gambling with his cash-strapped country's future and take crucial decisions needed to avert a devastating default.

However, an agreement between Greece and its international creditors is still possible and depends on political will, European Commission vice-president Valdis Dombrovskis has said.

“Negotiations are continuing on a technical level,” Mr Dombrovskis said at a joint news conference in Madrid with Spanish economy minister Luis De Guindos.

“Progress is possible and (an) agreement is possible. It really requires political will.“

A Greek source told Reuters that the IMF Greek delegation that had been negotiating a cash-for-reform deal had left Brussels for home on Thursday, citing outstanding disagreements.

“There are major differences between us in most key areas,” IMF spokesman Gerry Rice told reporters in Washington.

“There has been no progress in narrowing these differences recently and thus we are well away from an agreement.“

Greece needs a deal to unlock aid before the end of the month when it is otherwise set to default on a €1.6 billion repayment to the Washington-based IMF.

That could trigger capital controls and possibly send Greece hurtling towards an exit from the euro zone, with unpredictable consequences for financial markets and the European economy.

Mr Rice said the key sticking points remained pensions, taxes and financing. The IMF technical team had returned to the United States but remained “fully engaged” with Athens.

European stocks fell after the IMF comments.

Earlier, European Council president Donald Tusk spelled out an unprecedentedly forthright message to Greece's radical anti-austerity government after four months of bitter negotiations.

“There is no more time for gambling. The day is coming, I’m afraid, that someone says that the game is over,” he told a news conference after chairing an EU-Latin America summit that was dominated by intense talks with Tsipras on the sidelines.

“It is very obvious that we need decisions, not negotiations,“ Tusk said, adding that Athens needed to be “more realistic.”

Mr Tsipras held two hours of talks with European Commission President Jean-Claude Juncker, but neither side reported any breakthrough. “Come in the torture room,” Mr Juncker told Mr Tsipras at the start of their meeting.

EU officials later described the talks as a “last attempt” to reach a debt deal.

Asked about concerns for the process raised by the departure of IMF and Greek negotiators, an EU diplomat said: “If the process was working properly the president would not have had to have a meeting with Tsipras today.”

Mr Tsipras told reporters he had worked on bridging the remaining differences on fiscal and financing issues.

“We are working to assure an agreement which will ensure that Greece will recover with social cohesion and viable public debts,“ he said.

EU officials said the high-level Eurogroup Working Group, which prepares decisions for euro zone finance ministers, would discuss the IMF walkout at a meeting in Bratislava, Slovakia, on Thursday evening.

Tusk's dramatic admonition reinforced warnings by powerful German Bundesbank President Jens Weidmann and EU Economics Commissioner Pierre Moscovici that time was running out to avert a Greek state bankruptcy and possible exit from the euro zone.

Their stern tone contrasted with more optimistic noises from EU officials involved in the detailed negotiations with Greece, who said there was now a good chance of a deal in time for euro zone finance ministers’ next meeting on June 18 in Luxembourg.

Late-night talks between Mr Tsipras and the leaders of Germany and France produced no breakthrough, although all sides said they had moved closer on the procedure leading to an agreement.

"At the end of the talks there was absolute unanimity that Greece will work intensively and full steam ahead ... in the coming days to solve all remaining issues," German Chancellor Angela Merkel said.

To clinch a deal, EU officials said Tsipras’s government needed to offer alternative savings and tax measures to replace proposed pension cuts and tax rises he rejected as antisocial, to deliver a modest fiscal surplus before interest payments.

People familiar with the talks said the two sides have come closer to agreeing a primary surplus target but are still wide apart on how to achieve it, with EU and IMF experts doubting that measures touted by Greece can do the job.

More dire warnings rained down on the Greek leader as he contemplated what concessions to make to clinch a deal without alienating his left-wing supporters who elected him in January on promises to put an end to years of austerity.

“There is a strong determination to help Greece,“ the ECB’s Weidmann said in a speech in London. “But time is running out, and the risk of insolvency is increasing by the day.”

The main losers of a Greek default and euro exit would be Greece and the Greek people, he said.

“The contagion effects of such a scenario are certainly better contained than they were in the past, though they should not be underestimated,” Mr Weidmann said.

Moscovici urged Athens to come up with a list of economic reforms that could make a deal possible. “I really like Greek tragedy, but now we must move to the happy ending,“ he said.

Ms Merkel had made clear before the meeting with Mr Tsipras that Greece needed to satisfy the institutions representing the creditors rather than seeking a political fix on softer terms from her and French President Francois Hollande.

Tsipras renewed a call for a restructuring of Athens’ debts as part of any solution. The EU says that can only be considered after a deal to complete the existing bailout is secured.

Tsipras has denounced creditors’ demands to scrap an income top-up for the poorest pensioners and to refrain from unilateral moves to reintroduce collective bargaining or raise the minimum wage - policies that are anathema for his Syriza party.

Brussels says he is free to put forward alternative measures provided the numbers add up and yield a primary budget surplus.

The Greek leader faces pressure not just from left-wing hardliners but also from Greek voters, most of whom say they want to remain in the euro zone and want him to make concessions for a deal. Reuters