The eurozone's 19 leaders will meet in an emergency summit next week to seek a breakthrough in Greece's bailout talks following the latest failure to secure a deal that would prevent the country's bankruptcy.

Donald Tusk, who chairs meetings of European leaders, said he had decided to convene a eurozone summit for Monday evening to "urgently discuss the situation of Greece at the highest political level."

That means Greece's prime minister will meet with his peers, including German Chancellor Angela Merkel.

His statement came after the eurozone's top official, Jeroen Dijsselbloem, said no progress was made in discussions held among finance ministers in Luxembourg. He said Greece proposed too few measures that are credible and serious and that the talks over the past few weeks "have not progressed."

Greece needs outside financial help if it is to meet debt repayments this summer, starting with 1.6 billion euros ($1.8 billion) it owes on June 30. Without a deal it faces going bankrupt and even leaving the euro union.

Dijsselbloem said a deal was still possible and that he and his peers were "very committed" to keep Greece in the eurozone.

"Greece needs to become financially independent," he said. "Any deal that simply doesn't deliver that ... would be also a bad deal for the Greek people."

Officials acknowledged that Greece's exit from the euro - or "Grexit" - was now being discussed and that contingency plans were being made. As fears of a potential Grexit have swelled, there have been signs that Greeks are withdrawing money from their banks in increasing amounts.

Greece's radical left-led government has been locked in discussions with international creditors since its election in January over what economic reforms and budget cuts it needs to make to get the remaining 7.2 billion euros ($8.2 billion) available in its bailout fund.

The IMF said Greece's debt obligation at the end of the month is not up for negotiation.

"There is no period of grace of one or two months as I have read here and there," said the IMF's managing director, Christine Lagarde. "It's due on June 30."

The Greek government wants an end to the budget austerity measures that have accompanied the country's bailout loans for five years. It has also been seeking some sort of restructuring of the country's sky-high debt burden, which stands at near 180 percent of annual GDP. That could take the form of lower interest rates on the debt or extending the date by which the debts have to be repaid.