ATHENS—Greece's overwhelming rejection of creditors' demands in Sunday's referendum is a big win for Prime Minister Alexis Tsipras, but doesn't change what so far has been an impossible task: securing a place in the euro without accepting harsher austerity.

If the coming collision between Mr. Tsipras and his lenders leads to Greek debt default, bank failures and euro exit, Sunday's adulation could soon turn to fury, analysts said.

German-led creditor countries are staunchly opposed to financing a Greece that rejects a far-reaching, market-oriented overhaul of its economy.

Mr. Tsipras persuaded many Greeks to vote "no" on Sunday by arguing that such an outcome would strengthen his bargaining position vis-à -vis the rest of the eurozone and the International Monetary Fund. Following a "no" victory, he would reach a better deal with creditors within 48 hours, he said on Thursday.

Many Greeks trusted him to achieve the two outcomes they crave: an end to unpopular austerity measures such as pension cuts and a secure place in the euro.

Yet a swift deal is unlikely, European policy makers have made clear. Greece's bailout program, operating since 2010, expired on Tuesday. Athens must now apply for a new aid program from the eurozone's main bailout fund, the European Stability Mechanism, beginning a potentially lengthy negotiation process.

Germany and other lenders say they would continue to uphold the fundamental principle of eurozone bailouts since Europe's long debt crisis began: Rescue loans are only available in return for strict fiscal discipline and economic overhauls to make struggling economies such as Greece more competitive within the eurozone and the global economy.

At Mr. Tsipras's urging, Greek voters have now decisively rejected the very economic policies that Berlin and the IMF insist are essential if Greece is to achieve sustainable economic growth inside the eurozone.

Fresh financing appears more remote than ever. Time is running out before Greece must repay a large bond held by the European Central Bank that falls due on July 20. Default could lead to the ECB withdrawing liquidity support for Greece's banks, pushing them into insolvency. The banks have been closed for business for the past week.

The potential failure of Greece's banking system is the most likely trigger for a Greek exit from the euro, economists say. Without central-bank financing in euros, Greece would have to print its own currency to keep its banks alive.

Around 70% of Greeks want to keep the euro. Many would view an exit as a major betrayal and deception by a prime minister who promised them they could and should vote "no" and still keep the common currency.

The result is "an electoral win, but it could prove to be a debacle for the nation and potentially for him as well," said George Pagoulatos, professor of European politics and economy at the Athens University of Economics and Business.

"Support for the euro in polls is the highest it has ever been, so the result is a mandate to negotiate for a better deal within the euro," Mr. Pagoulatos said.

But creditors have warned over the past week that a "no" vote would amount to a rejection of the rules of nations' coexistence in the eurozone.

For some among the creditors, the damage may be irreversible.

Mr. Tsipras's provocative speeches over the past week, in which he accused creditors of blackmail, have helped his campaign for a "no" vote, but they also exhausted the meager goodwill of other eurozone governments toward the Greek leader.

Officials from Germany and other creditors have said the next bailout program—if there is one—would require tougher measures than those Greeks would have rejected in a "no" vote, because Greece's economic outlook is deteriorating because of its closed banks and capital controls.

"It is very likely he will end up with a deal that is worse from the one we turned down," said Loukas Tsoukalis, director of the Hellenic Foundation for European and Foreign Policy, an Athens-based think tank.

Matters could come to a head well before July 20, when Greece's ECB payment is due. Greek banks have scant cash left, and even with ATM withdrawals capped at €60 ($66) per card a day, their cash could run out within days, bankers say.

If the banks stop giving out cash, and no deal with Europe is in sight, the pressure on Mr. Tsipras could accelerate sharply, analysts said.

Write to Viktoria Dendrinou at viktoria.dendrinou@wsj.com

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