Greece will hold elections on June 17, and a court official will be appointed to head the interim government until then, Greek state television reported Wednesday.
Council of State head Panagiotis Pikramenos is to be named interim prime minister.
Communist Party leader Aleka Papariga said party leaders agreed that the interim government won't be able to make any internationally binding decisions. She spoke after a meeting of leaders convened by President Karolos Papoulias.
Uncertainty over the country's future — and therefore the economic future of the European Union — is expected to continue at least until the election results are known.
A nine-day deadlock in coalition negotiations after inconclusive elections forced Greece to hold the new elections.
The outright collapse of the European Union is being openly discussed as Greece sets up its caretaker government.
If left-wing parties take control after the June 17 election, it's likely the country will turn its back on austerity and the bailout it negotiated with the EU, analysts say.
That would almost certainly force Greece out of using the common European currency, the euro, which could unleash even more economic turmoil.
"The euro could disappear, and if the euro disappears, there is the danger that the whole European Union as such will disappear as well," Hans Stark, a political analyst with French Institute of International Relations (IFRI), said Tuesday in Paris.
"And that will be a new Europe — and maybe not such a comfortable one."
Concern over financial crisis
The head of the International Monetary Fund, Christine Lagarde, says Europe must be prepared for Greece to exit the eurozone, and warns that such a scenario would be quite messy.
On Wednesday, Greece's president is to convene the country's political leaders once more, this time to appoint a caretaker government that will lead the country into new elections next month.
The meeting follows the collapse of nine days of power-sharing talks made necessary by a May 6 election that left no party with enough votes for a majority in parliament.
The inability to form a government and the prospect of another inconclusive general election have increased concern over Greece's ability to cope with its severe financial crisis and threaten the country's continued participation in Europe's joint currency.
If the party leaders cannot agree on who will lead the caretaker government, the president will appoint the head of one of the country's top courts as interim prime minister.