Greece may default on its debts if a deal for more funding in exchange for fiscal reforms is not made. Here’s why that matters. (Jorge Ribas/The Washington Post)

Greece’s long-running standoff with its European creditors appeared headed on Saturday for an abrupt — and potentially cataclysmic — ending as the continent’s finance ministers rejected an emergency Greek request to help the cash-starved country meet a Tuesday deadline for paying back its debts.

The development, just hours after Greece’s prime minister stunned the continent with plans to hold a nationwide referendum on Europe’s latest proposals, makes it increasingly likely that Greece will default — and could soon crash out of the euro zone altogether.

Reflecting the newly dire outlook, people formed lines at ATMs across Greece, seizing on perhaps their last chance to withdraw their savings. Some went away empty-handed after the machines ran dry.

With speculation mounting that the banks may lack the funds to reopen Monday morning, European officials huddled behind closed doors to plot out how to contain the damage of a Greek financial meltdown. The Greek finance minister was pointedly excluded from those talks, which ended with a statement from the other 18 euro-zone countries urging Greek authorities to implement capital controls.

The statement also highlighted the safeguards that have been implemented to keep debt contagion from spreading to other vulnerable economies, suggesting that if Greece is forced to abandon the euro, the collateral damage may be limited. But because no country has left the euro zone in its 16-year history, no one knows just how extensive the impact may be.

The collapse of negotiations on Saturday was the most ominous turn in a process that has been poisoned from the start by bitter mistrust between Greece’s radical leftist government and the austerity-minded heavyweights who set policy in Europe.

Although both sides have repeatedly expressed a determination to keep Greece inside the common currency — and to avoid at all costs an uncontrollable and potentially disastrous default — that shared aspiration has not been enough to bridge the substantial divide.

As has become customary, each on Saturday blamed the other for the breakdown.

Greek Finance Minister Yanis Varoufakis called Saturday “a sad day for Europe” and said its decision to reject his request to extend Greece’s bailout for several more weeks “will certainly damage the credibility of the euro group as a democratic union.”

European officials countered that Greek Prime Minister Alexis Tsipras had blindsided them by calling a referendum early Sunday on a proposal that was still being negotiated, a move that effectively torpedoed any chance for a deal.

“The negotiations are clearly ended, if I understand Mr. Tsipras correctly,” said German Finance Minister Wolfgang Schäuble as the continent’s top finance officials gathered for their fifth emergency meeting in the past two weeks. “We have no grounds for further discussions.”

Varoufakis later challenged European leaders to come back with a new proposal and signaled an openness to further talks. But the acrimony with which talks ended Saturday suggested that a return to the negotiating table is highly unlikely before two critical tests in the week ahead.

The first will come Monday, when Greek banks that have grown ever more reliant on emergency loans from the European Central Bank face the prospect of reopening for business without new lifelines.

The second will be Tuesday, when a $1.7 billion payment to the International Monetary Fund comes due. The IMF has repeatedly said it will not offer an extension on that deadline. Greek officials, meanwhile, say they do not have the money to make the payment unless the country’s creditors unlock $8 billion in bailout funds that have been frozen as the negotiations have stalled.

Tsipras has set the referendum for July 5, although it is unclear exactly what Greek voters will be deciding. In announcing the vote, Tsipras said he wanted to give the Greek people the chance to vote on the latest proposal by Greece’s creditors, which he attacked as “an ultimatum” that would place “unbearable new burdens on the Greek people.”

But with Greece sliding toward default and a possible break with the euro zone, there is no guarantee that the offer will remain viable by the time of the referendum, even if Greece does vote “yes.”

The European Central Bank, the European Commission and the IMF have together provided Greece with $264 billion in bailouts over the past five years as the country has reckoned with sky-high debts.

After years of withering austerity policies imposed by European paymasters as a condition of those deals, Greece in January rejected the medicine and elected Syriza, a radical leftist party that promised to tear up the old agreements and start anew.

Greece has repeatedly demanded that Europe reduce the nation’s debt load and ease up on austerity, which officials say has devastated the economy and sent unemployment rocketing to 25 percent. But European officials have been unwilling to hand Syriza a victory and have insisted that the country keep to strict targets for belt-tightening.

The past week began with rare optimism, as Greece submitted proposals that European officials initially welcomed as a significant step forward after months of deadlock. But by Wednesday, the creditors had submitted counterproposals for slashing pensions and cutting spending. Greek officials rejected them, saying they would cross the government’s red lines.

During debate in the Greek Parliament on Saturday over whether the referendum should go ahead, Tsipras was given a standing ovation from supporters who cheered his defiance of European authorities. But opposition leaders and others accused him of recklessly endangering the country’s place in Europe.

“The nation’s most vital interests demand that the country remains at the heart of Europe. The E.U.’s actual shortcomings do not, in any way, negate this,” said former prime minister Costas Karamanlis, who spoke out after a long silence. “Foolish choices that undermine this principle push the country to adventures, with unpredictable and possibly irreversible consequences.”

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