The European Central Bank said on Monday it was keeping the level of emergency credit to Greek banks unchanged, putting the banks under increasing pressure as they try to cope with cash withdrawals.

The ECB said in a statement that the credit "can only be provided against sufficient collateral." That collateral has been weakened due to the worsening financial situation of Greece.

The decision leaves Greek banks in a stranglehold, as they struggle to replenish cash machines in the coming days.

The ECB says it is monitoring the situation in the financial markets closely and is ready to use all available measures to keep stability in the 19-nation eurozone.

Greece and its membership in Europe's joint currency faced an uncertain future, with time pressing for the country to reach a bailout deal with creditors after Greeks resoundingly rejected the notion of more austerity in exchange for aid.

With Greek banks running out of cash and facing the danger of collapse within days without new aid, the government in Athens is racing against the clock.

In an effort to facilitate negotiations on a new aid program Finance Minister Yanis Varoufakis, who had clashed with European officials in the bailout talks, announced his resignation Monday.

The Greek government named Euclid Tsakalotos as the new finance minister. The 55-year-old economist was Prime Minister Alexis Tsipras' lead bailout negotiator in talks that halted last month.

Greece and its creditors will meet again Tuesday to discuss how to keep the country in the euro. But the two sides remain far apart on key issues, particularly the notion of debt relief.

The negotiations are complicated for the European creditors by Tsipras' triumph in Sunday's referendum. More than 61 per cent of Greeks backed his call to vote "no" to budget cuts the creditors had proposed in return for rescue loans the country needs — even though those proposals were no longer on the table.

The vote was painted by opposition parties and many European officials as one on whether Greece should remain in Europe's joint currency. In the aftermath, many officials softened their tone and said talks would resume, though Greece's chance of staying in the euro was looking increasingly shaky.

The country's banks remained shut for a sixth working day on Monday as the government tries to limit a drain of deposits despite limits on cash withdrawals at ATMs. The banks will remain shut on Tuesday and Wednesday, as well.

Pensioners are given priority tickets as they wait to receive part of their pensions at a National Bank branch in Athens. (Christian Hartmann/Reuters)

The Greek government has vowed to quickly restart negotiations with creditors in other eurozone countries and with the institutions that oversaw the country's bailout: the ECB, European Commission and International Monetary Fund.

Varoufakis appared to be the first casualty of the vote's fallout.

With his brash style and fondness for frequent media appearances, Varoufakis had visibly annoyed many of the eurozone's finance ministers during Greece's debt negotiations.

Varoufakis said in a statement he was told shortly after the referendum result that some other eurozone finance ministers and the country's other creditors would appreciate his not attending the ministers' meetings.

Varoufakis defiant

The idea was one "that the prime minister judged to be potentially helpful to him in reaching an agreement. For this reason I am leaving the Ministry of Finance today," he said.

As for his European negotiating colleagues, he said of them: "I shall wear the creditors' loathing with pride."

With his high-stakes gamble to call a referendum with just a week's notice, Tsipras aimed to show creditors that Greeks, whose economy has been shattered and who face spiraling unemployment and poverty, have had enough and that the austerity prescribed isn't working.

Red spray paint covers a French-language Bank of Greece sign to read 'Bank of Merkel' in reference to German Chancellor Angela Merkel in Athens on Monday. (Thanassis Stavrakis/The Associated Press)

But everything hinges on European reaction. A eurozone summit was hastily called for Tuesday afternoon to discuss the situation.

European officials appear to be split on a key demand by Greece to have the burden of its bailout loans be made more manageable.

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."

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Sapin also called for the ECB to maintain liquidity assistance to Greek banks.

Germany, however, remains reluctant to discuss debt forgiveness.

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

France, Germany say situation is urgent

The leaders of Germany and France said Monday they respect Greece's vote against the terms of an international bailout, and added the door remains open to negotiations with the Greek government to find a way to keep the country in the 19-country eurozone.

While thousand of Greeks took to the street to celebrate the results, the country is still facing overwhelming public debt and a possible exit from the eurozone. (Christopher Furlong/Getty Images) German Chancellor Angela Merkel stressed the importance of Greece taking "responsibility" for reforming its economy, while French President Francois Hollande said it is important for Europe to show "solidarity" with Greece. The two leaders run the eurozone's largest economies.

The two leaders met in Paris on Monday. Their brief statement set the tone for Tuesday's emergency summit in Brussels of the eurozone's 19 national leaders.

Both stressed the urgency of coming to a decision on a solution to Greece's financial woes, with Merkel demanding proposals from Greece's prime minister this week.

Besieged by a prolonged recession, high unemployment and banks dangerously low on capital, Greece defaulted on an IMF loan repayment last week, becoming the first developed nation to do so.

Now some analysts wonder if Greece is so starved of cash that it could be forced to start issuing its own currency and become the first country to leave the 19-member eurozone, established in 1999.

Tsipras was elected in January on promises to repeal the austerity demanded in return for its bailout and negotiations broke down late last month after dragging on unsuccessfully for five months.