By Gabriele Steinhauser in Brussels and Andrea Thomas in Berlin 

Germany stood firm against debt relief for Greece the day after the country's voters issued a resounding "no" to more austerity, signaling a tough fight ahead on one of the few opportunities for compromise on any potential bailout for Athens.

About 61% of Greek voters cast their referendum ballots on Sunday in support of Prime Minister Alexis Tsipras's stance against the pension cuts and tax increases that Greece's creditors--the rest of the eurozone and the International Monetary Fund-- say are necessary to get Greece's economy going again.

That leaves cutting debt as a possible make-or-break element of any deal to keep Europe's currency union intact.

German Chancellor Angela Merkel and French President François Hollande, whose country has emerged as one of the few friendly voices for Greece in the eurozone, made no mention of the debt issue at a joint news conference in Paris.

But opposing comments from their finance ministries earlier in the day suggest that the question will be a major theme at a summit of eurozone leaders on Tuesday.

"We have shown a lot of solidarity with Greece and the last offer [for more bailout aid] was also a generous offer," Ms. Merkel told journalists after the one-hour meeting. "At the same time, Europe can only hold and stand together ... if every country lives up to its own responsibility."

Ms. Merkel and Mr. Hollande said it was now up to Greek Prime Minister Alexis Tsipras to make clear proposals on what his government is prepared to do in return for renewed support from the other 18 eurozone countries.

"Time is pressing here and it is important to us that such proposals must come this week so we can resolve the situation as it presents itself currently," Ms. Merkel said.

Raising expectations on the possibility of resuming negotiations, the country's confrontational Finance Minister Yanis Varoufakis resigned on Monday under pressure from Mr. Tsipras and creditors. Though extremely popular at home, Mr. Varoufakis has exasperated European colleagues with his blunt talk and confrontational style since taking the job in January.

Finding a solution to Greece's financial crisis is urgent if Europe wants to keep its currency union intact. The eurozone portion of Greece's EUR245 billion ($271 billion) bailout has expired, and a default on a EUR1.56 billion payment to the IMF last week means Athens isn't eligible for any more loans from the fund. A crucial EUR3.5 billion bond repayment to the European Central Bank is due July 20.

Some relief for Greece--whose debt load stood at 177% of gross domestic product at the end of last year--would allow Mr. Tsipras to deliver new concessions to the country's voters. But it could prove expensive for other governments, both financially and politically. Initial reactions Monday pointed to a split between the eurozone's two biggest economies.

"A haircut [on Greece's debt] is not on the table for us," Martin Jäger, the spokesman of German Finance Minister Wolfgang Schäuble said, reiterating the long-held view of the government.

France's finance minister was more sympathetic. "I've always said talking about debt is not a taboo," said Michel Sapin. "The burden of debt in the coming months and years is too high for Greece to be able to pick itself up again."

Any deal on the debt would have to come as part of a broader agreement on more bailout aid. In the coming years, Greece has to repay billions of euros of old loans from the IMF, which likely wouldn't be included in any restructuring.

Germany's vice chancellor and leader of the Social Democrats, Germany's junior coalition partner, struck a pessimistic note on the likelihood of reaching a deal before the next big payments to creditors.

"The ultimate insolvency of the country seems to be imminent," said Sigmar Gabriel, who is also Germany's economic minister. "We all know that it is pretty much impossible" for Greece to pay back its debt in the near- and long-term, he said.

Any proposals on how a financial breakdown could still be avoided would have to come from the Greek side, Mr. Gabriel said. "The ball is now in Athens's court," he said.

The first outlines of Greece's plan were emerging Monday. In a rare sign of unity, Mr. Tsipras and the leaders of the opposition party decided in a seven-hour meeting that Greece's common goal is to cover financing needs and go ahead with reforms "with the least possible recessionary impact." A Greek government official said that the plan included a commitment to restructure the debt.

There are alternatives to a straight-out reduction in the face value of the eurozone's rescue loans to Greece. In 2012, when the country last came close to default, the currency union's finance ministers promised to take measures to bring the country's debt to below 110% of GDP within 10 years, for instance by giving it more time to pay them back or further lowering interest rates.

Letting its eurozone bailout expire last week means that "this offer is not on the table anymore now," Valdis Dombrovskis, the European Commission's vice president of the euro, said. But Mr. Dombrovskis said that past discussions have shown that "eurozone countries are ready to look at the Greek debt, at the conditionality of the Greek debt, at the debt settling costs."

The European Central Bank tightened the screws on Greek banks on Monday by raising the amount of collateral they must post to secure the emergency lending that is keeping them alive. It also decided to maintain the cap on the emergency loans that has been in place for more than a week.

Greek banks have been closed since last week and ATM withdrawals have been limited to EUR60 euros a week to stem the flow of money that Greeks had been pulling out of the banks, and financial paralysis could worsen. The head of the country's banking association told reporters Monday that banks would remain closed through Wednesday; few expect them to open any time soon after that.

The IMF has long insisted that high debt has been weighing on growth and that the currency union's governments should take action to reduce it. In an analysis of the country's debt path over the coming decades released last week, the IMF said that even if Athens implements the rejected measures, the eurozone would need to double the maturities of its rescue loans to Greece to 60 years.

If budget and overhaul targets were weakened further, the IMF warned, governments might have to write off some EUR50 billion of the EUR184 billion they have already lent Greece. That report was seized on by Mr. Tsipras and other members of his government in their "no" campaign.

William Horobin

in Paris and Nektaria Stamouli and Stelios Bouras in Athens contributed to this article.

Write to Andrea Thomas at andrea.thomas@wsj.com