* Euro zone, Greece face off after months of "poker"
* Anger at Greek government evident, despite fear of risks
* Unclear how coming days will affect currency bloc
* Wider concerns raised about future of European Union
BRUSSELS, June 28 (Reuters) - Europe's grand project to bind its nations into an unbreakable union by means of a common currency lurched into uncharted waters after EU governments refused funding to save Greece from defaulting on its debts.
While finance ministers of the other 18 euro zone states chorused their insistence that Greece would remain inside the bloc, exasperation with the leftist government's decision to reject creditors' final offer and instead call a referendum was manifest and some officials spoke privately of expelling Athens.
"They were playing poker," said Austrian Finance Minister Hans Joerg Schelling after the Euro group that runs the currency met on Saturday without their Greek counterpart to discuss how to limit the fallout. "But in poker, you can always lose."
After five months of halting negotiations with a Greek government elected to end the pain of austerity measures, EU leaders left a summit in Brussels on Friday believing that a deal was close to roll over bailout funding and let Athens meet a repayment to the IMF on Tuesday and further obligations over the coming months.
But Prime Minister Alexis Tsipras provoked consternation by returning home to call a referendum for next Sunday on the offer and urging voters, weary of years of debt crises, to reject it.
"Tsipras messed up," one EU official said. "We did everything possible. They chose to blow up when we were so close to settling this in a way that would allow them to sell it."
Amid political drama in Greece, where a clear majority wants to remain inside the bloc, the next few days present a major challenge to the integrity of a 16-year-old currency bloc, which many blame for massive unemployment in countries outside Germany and its neighbours in the richer north and west of Europe.
"We must do everything we can to fight any conceivable threat of contagion," German Finance Minister Wolfgang Schaeuble said after a meeting at which the group effectively called for capital controls to ring-fence Greek banks haemorrhaging cash.
While acknowledging that only Greece - or possibly banks themselves - can instigate such a shutdown, the ministers said the European Central Bank, whose management meets on Sunday, should use its powers to stabilise markets.
"You have to count on Greece getting into acute problems in the coming days because of this decision," said Schaeuble, some of whose conservative allies have made no secret of preferring to see Greece forced out of the euro zone. "That is difficult as we do not know how it will live up to its commitments."
He and others, however, stressed their faith in stability mechanisms put in place after scepticism among investors pushed the euro zone to breaking point following a run of national bankruptcy scares in the wake of the global crash of 2008.
And, echoing his French Socialist counterpart, Michel Sapin, Schaeuble insisted after the fifth such deadlocked ministerial meeting in just over a week: "Greece remains a member of the euro zone and Greece remains part of Europe."
But few EU leaders now trust this Greek government, whose calls for debt relief and criticisms of the bailout's deadening effect on growth have been echoed by some leading economists.
When representatives of the three creditor institutions - euro zone governments, the ECB and IMF - met after Greek Finance Minister Yanis Varoufakis had left, participants quoted one senior official as joking that at least they could refer again to the lenders as the "Troika," a term Varoufakis had insisted be dropped because Greeks associated it with external diktats.
Dutch Finance Minister Jeroen Dijsselbloem, the Euro group chairman, repeatedly referred to the possibility that the Greek parliament might reject Tsipras's call for a referendum. But lawmakers dashed any prospect of a quick shift in Greek politics before markets open on Monday by voting for it to go ahead.
Still, Dijsselbloem insisted: "The process has not ended. It will never end probably. We will continue to work with Greece. Many things could happen, many scenarios are conceivable."
As Greeks lined up to take cash from ATMs, it remained to be seen how financial mechanisms would work. If Greece fails, as it has said it will, to repay 1.6 billion euros to the IMF on Tuesday, that default can have knock-on effects.
Some experts speculate that Greece could formally remain in the euro zone but issue its own IOUs to pay immediate bills.
The ECB must also decide whether to keep supplying liquidity to Greek banks, once the government whose debt makes up a large chunk of their assets is no longer meeting its obligations and once the bailout programme formally expires on Tuesday.
The central bank, under its president, Mario Draghi, has been reluctant to take such a highly politicised decision. At the same time, political leaders have been reluctant to override the decisions of finance ministers lest that appear to be a signal that the rules of the common currency are open to manipulation.
Donald Tusk, a former Polish prime minister who chairs meetings of the 28 EU leaders, made clear at two summits in the past week that heads of government must nonetheless take their responsibilities in a crisis that affects the Union as a whole.
Early on Sunday, he was in contact with leaders again: "Greece is and should remain euro area member," Tusk tweeted.
The Greek government's demands have alienated its euro zone partners - from Germany and its northern allies, to southern states and Ireland whose governments face critics of their own bailout terms to easterners much less prosperous than Greece.
But with Britain already planning a referendum on leaving the EU, a breach in formal institutions worries those who fear economic drift. Complaints it lacks democratic accountability threaten the EU's survival in its present form.
One official close to Saturday's Euro group discussions said the issue of Greece leaving the euro, or the EU, was not raised - there is no obvious legal way to force it out of either. But, the official said, a "Grexit" could not be entirely ruled out.
Leaving Brussels on what he called a "sad day for Europe," the outspoken Varoufakis warned that the rift with Athens would damage the euro zone's credibility as a "democratic union" - "And I'm very much afraid that that damage will be permanent."
(Additional reporting by Jan Strupczewski, Robert-Jan Bartunek and Andreas Rinke; Editingn by Steve Orlofsky)