ATHENS—Greeks overwhelmingly voted against their international creditors' conditions for further bailout aid, in a result that could deepen the rift between Greece and the rest of Europe and push the country closer to bankruptcy and an exit from the euro.

More than 61% of Greeks voted "no" in Sunday's referendum on austerity measures and other overhauls that European and International Monetary Fund officials had demanded in recent talks—an outcome that spurred popular celebrations into the night across downtown Athens and other Greek cities.

"I trust this man," said Zoe Vergaki, a young musician among Greek Prime Minister Alexis Tsipras's cheering supporters on the capital's Syntagma Square. Nearby, some danced to the music of "Zorba the Greek." "Whatever deal he brings," Ms. Vergaki said of the leftist premier, "I will support him."

Greeks' resounding rejection of creditors' demands for pension cuts, value-added tax increases and other austerity measures is likely to bolster the conviction of the Athens government that it can now successfully press its creditors for a better bailout deal that includes fewer painful fiscal measures and more debt relief.

"I'm fully aware that the mandate that I was given (by voters) is not for a rupture with Europe, but a mandate boosting our negotiating strength for reaching a sustainable deal," Mr. Tsipras said in a televised message late on Sunday.

That may prove a hard sell in Germany and many other creditor countries, where many policy makers are likely to view the referendum result as proof that Greece doesn't want to adhere to the common rules of the eurozone.

The stability of the eurozone could now hinge on whether Greece and its creditors can find a way out of their dangerous impasse. Hard-line eurozone policy makers, led by German Finance Minister Wolfgang Schä uble, believe that expelling Greece for its recalcitrance would strengthen the eurozone and put pressure on other economically underperforming countries—including Italy and France—to reform, officials in Berlin say.

Other German officials say that Chancellor Angela Merkel worries that the precedent of a Greek euro exit could make the currency union chronically brittle, inviting speculation against other euro members in future financial crises. Ms. Merkel has long been Europe's most powerful advocate of keeping Greece in the eurozone. But her stance has shifted closer to Mr. Schä uble's in recent weeks, however, as Mr. Tsipras's confrontational tactics have aroused the ire of German voters and lawmakers.

Sunday's collision between the expression of the popular will in a small European country and the economic-policy consensus of Europe's political establishment could make the eurozone debt crisis even more intractable.

Willingness to make politically difficult compromises is dwindling in both Greece and among its creditors. Avoiding a financial and economic meltdown in Greece would likely require a level of flexibility that none of the important actors in the latest Greek drama have shown over the past year.

Mr. Tsipras is expected to seek a new bailout program from Europe and has promised Greeks that he can reach a deal in as little as 48 hours after the referendum. That is highly improbable, European officials say. Indeed, the challenge for Mr. Tsipras will be to reach a deal at all, these people say.

Creditors have warned that any further bailout aid will come with even more strings attached—the opposite of Mr. Tsipras's promises to Greeks.

Greece's economy, already back in recession this year after a brief recovery in 2014 fizzled out, is now suffering a fresh blow—thanks to capital controls and closed banks. Financial paralysis could worsen in the week ahead as cash in the banking system runs short.

A weaker-than-expected economic outlook would entail even more budget measures to achieve the fiscal surpluses before interest that creditors are insisting on.

Any bailout deal would also require the IMF and eurozone governments, led by Germany, to overcome their dispute over Greece's debt. The IMF insists that "comprehensive" debt restructuring is now needed to make Greece solvent. European governments have refused so far to discuss any debt relief for Athens that would impose overt losses on their own taxpayers.

Mr. Tsipras's greatest problem in striking a deal may well be that other European leaders don't trust him to implement the tough economic policies they want—even if he were to sign up to them in principle.

Goodwill toward Mr. Tsipras and his ruling left-wing Syriza party was already in short supply in most European capitals. But Mr. Tsipras's decision to call a referendum just over a week ago, as Greece's European bailout program was about to expire, and to campaign against creditors' economic demands caused fury around eurozone capitals, including inside the German chancellery, European officials say.

Eurozone leaders are now expected to meet on Tuesday evening in Brussels to discuss the aftermath of Greece's referendum.

Time to repair relations and strike a deal is short. Greece must repay a €3.5 billion bond held by the European Central Bank on July 20, and another large ECB-held bond that falls due Aug. 20. Without a bailout deal, Athens faces default on those bonds.

A Greek default would put heavy pressure on the ECB to reject Greek government-backed debt as collateral for liquidity for Greek lenders—a move that would likely cause the country's banks to collapse.

A failure of the Greek banking system has long been viewed by economists as the most likely trigger for Greek exit from the euro. If unable to raise fresh money in euros to save its banking system, Greece would likely be forced to print its own national currency.

The situation could come to a head well before Greece's ECB bonds are due. Louka Katseli, chairwoman of Greece's largest bank, told reporters on Friday that Greek banks had enough cash to continue doling out money to depositors through Monday. By Tuesday, they may not have any left.

Mr. Tsipras is now likely to look to Chancellor Merkel to offer him a bailout that involves less austerity and more debt relief—as he has done for months.

But Ms. Merkel last week emphasized the principle she has insisted upon ever since the Greek crisis began in late 2009: Germany is prepared to finance other euro nations only in return for far-reaching economic overhauls, including as much austerity as is needed to close budget deficits.

Breaking that rule would do more damage to the eurozone than letting a country that rejects the rules go, Ms. Merkel told Germany's parliament last week.

Mounting anger among German voters, media and lawmakers against Greece's Syriza-led government also limits Ms. Merkel's scope for offering Mr. Tsipras more-generous bailout terms. German public and elite opinion is strongly opposed to forgiving any of the country's loans to Athens.

The tensions among Athens, Berlin and the IMF that have made an agreement elusive all year haven't been reduced by Sunday's referendum.

If anything, the emphatic proof of Greek popular support for Mr. Tsipras's hard line against creditors could make him even less willing to bend, and the dispute more intractable.

How the ECB reacts to a potential Greek bond default on July 20 depends on the political context, European officials say. If there is progress toward a financing agreement between Athens and other eurozone governments, then the ECB is more likely to use all available flexibility in its rule book to continue supporting Greece's banks.

But a continued standoff between Mr. Tsipras and his European peers would make it difficult for ECB President Mario Draghi to justify further liquidity support for Greek banks to his increasingly impatient governing council, ECB officials say.

Mr. Draghi is reluctant to be seen as the person to push Greece out of the euro, say people familiar with his thinking. Instead, he is likely to pass responsibility for any such decision to eurozone governments by requesting that they guarantee Greek liabilities. If such a guarantee isn't forthcoming, the ECB could argue that European leaders have taken a political decision to cut Greece loose, these people say.

Viktoria Dendrinou and Marcus Walker contributed to this article.

Write to Nektaria Stamouli at nektaria.stamouli@wsj.com and Stelios Bouras at stelios.bouras@wsj.com

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