The European Central Bank has agreed to increase its emergency support for Greece's banking sector after fears of a Greek exit from the euro led to a run on the banks.

The Bank of Greece insisted on Friday that the country's banking system was stable, but sources said it appealed to the ECB.

The new ECB funding is believed to be worth up to $3.4bn, and is expected to tide the banks over only until Monday, when more may be needed.

That's still less than the $4.2bn that customers have withdrawn from Greek banks in the last week.

GREECE BY NUMBERS Greece has less than two weeks to come to an agreement with its creditors or risk defaulting on $1.8bn of loan repayment.

It owes more than $378bn to the International Monetary Fund, the European Central Bank and the European Union for the bailouts it received in 2010 and 2012.

According to some estimates the debt burden equals more than $34,000 for each Greek citizen.

And it's almost twice the amount of money currently at the centre of the impasse - the $1.8bn repayment the Greek government is due to make to international lenders by the end of the month.

Greece said on Friday it was still hopeful for an 11th-hour deal with its creditors before it defaults on its debt.

"Those who invest in crisis and terror scenarios will be proven wrong," Prime Minister Alexis Tsipras' office said, amid reports that Greeks banks were facing an increase in withdrawals.

EU President Donald Tusk has called an emergency summit of the leaders of the 19 eurozone countries in Brussels on Monday after finance ministers failed on Thursday to break the five-month deadlock between the anti-austerity government in Athens and its international creditors.

French President Francois Hollande said on Friday that "everything" must be done to seal a compromise on the Greek debt crisis.

Economic powers outside the eurozone were also watching the situation with growing alarm, with the US saying there is "an urgent need for both Greece and its international partners to take steps towards compromise".

However, in a move that seemed calculated to irk other European leaders amid tensions with Russia over Ukraine, Tsipras visited Saint Petersburg as the star guest at President Vladimir Putin's investment drive forum.

The two sides sealed a preliminary agreement to set up a joint venture to extend the TurkStream gas pipeline through Greece.

End of the eurozone

Greece has little time left to agree to a reform deal in order to secure the remaining portion of its multibillion-dollar bailout, which it needs to avoid defaulting on a debt payment of around $1.8bn to the International Monetary Fund due on June 30.

Expert: Creditors don't want Greece out of the euro

Analysts have long warned that a default may set off a chain of events leading to a "Grexit" - Greece leaving the eurozone, and even the Bank of Greece warned that would be the likely result.

"I repeatedly warned Mr Tsipras that he cannot rely on me to prevent a collapse of talks," Tusk said.

Tsipras, who was elected on an anti-austerity promise in January and who has been reluctant to accept a deal that would raise taxes and cut spending further, warned in turn that Greece's exit would lead to the undoing of the euro.

"The famous Grexit cannot be an option either for the Greeks or the European Union. This would be an irreversible step, it would be the beginning of the end of the eurozone," Tspiras told the Austrian daily Kurier on Friday.

Creditors have refused to pay the remaining $8.21bn if there is no deal, and the cash will be lost forever to Greece if there is no agreement for an extension.

Greece has to pay another $7.6bn to the ECB in July and August.