There will be a solution to the Greek debt crisis that will allow the country to return to growth while staying in the euro zone, Prime Minister Alexis Tsipras said on Friday, as the country moved closer to the brink of default.

Tsipras's tone was strikingly upbeat given that talks over a cash-for-reforms deal for Greece remained deadlocked after a meeting of euro zone finance ministers and that bank withdrawals from Greek lenders have accelerated in the past week.

The leftist leader, who has refused to make concessions over tax hikes and pension reforms demanded by Greece's creditors, welcomed a planned euro zone emergency summit on Monday and dismissed those predicting catastrophe.

"The leaders summit on Monday is a positive development on the road toward a deal," Tsipras's office said in a statement. "All those who are betting on crisis and terror scenarios will be proven wrong."

"There will be a solution based on respecting EU rules and democracy which would allow Greece to return to growth in the euro."

Time is running out for Greece to strike a deal and avoid defaulting on a 1.6 billion euro loan to the International Monetary Fund by the end of June – the first in a series of looming payments for the cash-strapped country.

The IMF chief raised the stakes on Thursday by telling Greece there would be no grace period or delay permissible in repaying the money.

The ECB's governing council will hold a telephone conference on Friday to discuss extending emergency liquidity for the lenders, sources said.

With the health of Greek lenders increasingly in peril, one executive board member of the European Central Bank questioned on Thursday whether Greek banks would be able to open next week.

European Council President Donald Tusk has convened Monday's emergency euro zone summit to discuss Greece "at the highest political level".

Greek savers pulled out some 2 billion euros between Monday and Wednesday after weekend negotiations collapsed in Brussels, senior banking sources told Reuters. That is double the amount that the ECB granted Greek banks in extra emergency liquidity assistance (ELA) only on Wednesday.

If deposit flight continues to outpace ELA, it could force Greece to impose capital controls, as Cyprus did in 2013, to ration cash withdrawals.