ATHENS, Greece -- Despite triumphing in a popular vote against austerity, Greece on Monday faced the urgent need to heal its ties with European creditors and reach a financial rescue deal that might prevent it from falling out of the euro -- possibly within days.

Prime Minister Alexis Tsipras won big in Sunday's referendum, in which 60 per cent of Greeks rejected the economic measures creditors had proposed in exchange for loans the country needs to remain afloat. He also received the rare backing of opposition parties to restart bailout negotiations.

But his bolstered mandate to push for better concessions from creditors hit the hard reality of the country's deteriorating finances, with the banks facing the risk of collapse within days unless a rescue deal is reached.

In a sign that he hopes to reach a deal as soon as possible, Tsipras appointed a new mild-mannered finance minister to lead talks with bailout creditors and replace Yanis Varoufakis, the hard-talking professor who clashed regularly with his European counterparts.

Euclid Tsakalotos, a 55-year-old economist, appears more willing to reach a compromise with creditors and will be tested as soon as Tuesday, when he will meet the other 18 eurozone finance ministers in Brussels.

That meeting is meant to seek the basis for a deal that European leaders, including Tsipras, might discuss at an emergency summit later in the day. Ahead of the summit, Tsipras spoke by phone with German Chancellor Angela Merkel.

Greece's financial situation is getting more difficult by the day. It had to close the banks last week to prevent their collapse in the face of a run, and imposed limits on cash withdrawals and transfers.

Greek banks remained closed Monday, with only a few branches opening for pensioners to receive emergency assistance. Louka Katseli, head of the Greek Bank Association, said she expected banks to remain closed for at least two more days.

The government is expected to extend the restrictions on withdrawals after the European Central Bank makes a decision later Monday on cash support for Greek banks.

The ECB has frozen the amount of credit it allows Greek banks to draw on, even though their cash requirements are growing as people rush to withdraw what money they can.

Analysts say that if the ECB keeps the amount of credit on hold, Greek banks will come under increasing pressure and the government could have to make the limits on cash withdrawals even tougher.

The ongoing Greek drama hurt stocks around the world, particularly in Europe. The losses were not as great as some had feared, however, suggesting investors think that a Greek exit from the euro, while devastating for the country and destabilizing in Europe, would be manageable for the global economy.

"The 'no' vote in Greece's referendum on Sunday dramatically increases the risk of a slide toward a disorderly Greek exit from the eurozone," ratings agency Fitch said.

"An agreement between Greece and its official creditors remains possible, but time is short and the risk of policy missteps, or that the two sides simply cannot agree a deal, is high."

With all ballots counted, 61.3 per cent of voters in Sunday's referendum said "no" to the question of whether they would accept creditors' proposed measures.

Tsipras has agreed to imposing more harsh austerity measures, following a six-year recession, but wants eurozone lenders to grant the country better terms for bailout debt repayments.

"The prime minister is ... committed to starting a fundamental debate on dealing with the problem of sustainability of the Greek national debt," a statement signed by the government and three pro-European opposition parties said.

European officials appear to be split on Greece's demand for easier debt repayment.

France's finance minister, Michel Sapin, indicated that discussing Greece's debt is not taboo, saying the country could not recover with its current obligations "in the months and years to come."

Germany, however, remains highly reluctant to discuss debt relief.

Finance Ministry spokesman Martin Jaeger said Germany's "position is well-known ... a debt cut is not an issue for us."

German Vice Chancellor Sigmar Gabriel said Europe should be preparing to help Greeks with humanitarian assistance.

"The situation that is now being created by the referendum makes me sad, because life for the Greek population is going to get harder in the coming days and weeks," he said.

"After yesterday's celebrations in the streets there's a danger of a rude awakening soon."