Greece and its European lenders prepared for a final showdown over whether to keep this struggling Mediterranean nation in the euro zone, amid signs that the economy would asphyxiate within days without a desperately needed bailout.

Facing a Thursday deadline to submit a full plan and a Sunday end-date to strike a final deal or risk the collapse of its financial system, Greece on Wednesday officially asked its European partners for a new three-year rescue. In a one-page letter, ­obtained by The Washington Post, Greece promised to take fresh steps on contentious issues such as taxes and pension payouts as early as next week. It also pledged to take unspecified “additional actions” to “strengthen and modernize” its nearly bankrupt economy.

Greece, though, said it would not provide full details until Thursday, leaving European leaders guessing whether Athens was truly prepared to make tough sacrifices to win a new deal less than a week after Greek voters resoundingly rejected a previous cash-for-cuts offer by its euro-zone partners. For their part, officials said that although they wanted to keep Greece in the euro zone, they were also prepared to let it go.

Athens also did not specify the size of its bailout request. But the International Monetary Fund has said it needs at least $66 billion through 2018 along with far more generous payment terms.

Yet the Tuesday decision by European leaders to impose hard deadlines on Greece — which it must meet or risk a possible end to aid for its banks from the European Central Bank and ejection from the euro currency union — raised the prospect of a potentially ugly endgame to a 5½-year debt crisis. In Washington, alarm was mounting that the crisis was entering a dangerous stage of brinkmanship, with new and uncertain risks for Europe and global markets.

Greeks overwhelmingly voted against a strict bailout package proposed by the E.U. Here is how that affects Greece and the United States. (The Washington Post)

“The risk of an accident goes up dramatically when you create more of these kind of life-and-death deadlines,” U.S. Treasury Secretary Jack Lew said in comments at the Brookings Institution in Washington on Wednesday.

In Athens, concern was also clearly growing. The ECB declined on Wednesday to increase its lending to embattled Greek financial institutions, leaving banks to extend closures that began June 29 through at least Friday. ATM limits of 60 euros per day per customer were extended through Sunday, even as some pharmacies began complaining of shortages of medicine.

At one pharmacy off the city’s main Syntagma Square, druggist Ion Oikonomakis had to turn away two customers seeking asthma and pain medicine on Wednesday. The 52-year-old said he was unable to import the drugs because of the new limits on the flow of cash.

Oikonomakis said he was convinced the country would soon be forced to return to its former currency, the drachma. He blamed Greece’s overly generous pension benefits for the country’s economic struggles. Retirees are a key voting bloc, and politicians are only too ready to pander to them, he said.

“Nobody can pay for all these people,” he said.

In Washington, Lew also appeared to support a controversial assessment from the IMF that Greece’s 320 billion euro ($355 billion) debt load was so unsustainably large that some form for debt forgiveness by its creditor nations was now inevitable. That position is considered highly controversial in some countries in Europe, chiefly Germany, whose hardworking taxpayers may need to bid auf Wiedersehen to billions of euros under such a deal.

Nevertheless, some key European decision makers — most important, France — sounded new notes of optimism that a deal could be reached. And Greek officials, who have demanded debt relief in exchange for any fresh cuts, also signaled they may be willing to accept a pledge for debt forgiveness later this year rather than an immediate concession to secure a quick deal.

But serious doubts remained whether the Greek proposal would go far enough to assuage concerns in Germany, Greece’s largest creditor nation, whose chancellor, Angela Merkel, will be the chief decider on any deal.

“The chancellor has always maintained that the fundamental principle must be aid against reforms, and I do not think that she is ready to give up this position,” said Nicolai von Ondarza, a policy analyst at the German Institute for International and Security Affairs. Even if Merkel did, he cautioned, German lawmakers — who must give their approval to any deal — are unlikely to be as forgiving.

Last week, Merkel had largely succeeded in securing widespread backing in Europe for Berlin’s hard-line position that a no vote in Greece against austerity in last Sunday’s referendum would effectively be a choice to leave the euro.

But since the vote, France and other nations appear to have been deeply struck by fears that a Grexit — or Greece exit from the euro zone — is no longer a theoretical possibility. Such an event, they fear, could affect the future of European economic and political unity and create a failed state on Europe’s southeastern flank. So deep is French concern that it has offered technical assistance to the Greeks as they seek to put a new proposal forward.

“Keeping Greece in the euro and, therefore, in the heart of Europe, and the E.U. is something of the utmost geostrategic and geopolitical importance,” French Prime Minister Manuel Valls told lawmakers in Paris on Wednesday. “Allowing Greece to exit the euro zone would be an admission of impotence — France refuses that.”

With the Greek economy on the verge of free fall, Prime Minister Alexis Tsipras issued an impassioned plea for a new deal to the European Parliament in Strasbourg, France, provoking both ­applause and boos, and touching off a fiery day of debate over his tactics.

“We will continue with our reforms undertaken, but let us not forget that the Greek people have made a tremendous effort for adjustment,” he said. “This has exhausted the resilience and patience of the Greek people.”

But even as Tsipras spoke in Strasbourg, his allies back home recognized that Greece’s bargaining position was poor, despite Sunday’s landslide rejection of austerity. Several of Tsipras’s closest allies said their strongest argument to Europe was that if Greece were kicked off the euro, further economic turmoil would befall the remaining euro zone nations.

“We know that we are the weak player in the game,” said Greek Labor Minister Panos Skourletis. “If we have an agreement, we will have austerity measures.”

He said that Tsipras was willing to concede on austerity if he won some reprieve for Greece’s towering pile of debt. Above all, Greece needs a deal, he said, because within weeks it may not even have the cash to pay pensions. “I believe we have enough until the end of July,” he said.

Ylan Mui in Athens and Stephanie Kirchner in Berlin contributed to this report.

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