Nine days after inconclusive elections, the leaders announced they had been unable to forge the necessary consensus to create a coalition during emergency talks on Tuesday led by the president, Karolos Papoulias.
The collapse of talks, after a week of abortive attempts by individual leaders to form an administration, sent global financial markets diving.
Attributing the breakdown to "petty party interests", Evangelos Venizelos, who heads the socialist Pasok party, said the only way out of the impasse was to hold fresh elections next month.
The new poll is expected to be announced on Wednesday and will take place on 10 or 17 June, officials said.
A caretaker government will replace the outgoing left-right coalition, led by the technocrat banker Lucas Papademos, as the nation prepares for another round of election campaigning.
"Unfortunately the country is being led again to elections ... under very bad conditions," said Venizelos, adding that he hoped the next decision of Greek voters would be "more mature".
"The country can find its way again," the politician insisted, before urging citizens to read the minutes of the two-hour-long talks. "Let's choose to go towards the better. In God's name, let it not be worse."
Like its longtime rival New Democracy, Pasok was pummelled in the 6 May election, a ballot that will be remembered for reconfiguring Greece's political map.
Voters enraged by more than two years of unprecedented belt-tightening enforced by mainstream forces to try to keep the economy afloat, elected to support anti-austerity fringe parties on the left and right. No group won enough votes, however, to have a working majority in Athens' 300-seat parliament.
Amid heightened concerns over Greece's place in the eurozone, the prospect of further political uncertainty could not come at a worse time.
Athens is not only dependent on rescue funds from its "troika" of creditors - the European Union, the European Central Bank and the International Monetary Fund - who rushed to prop up its ailing economy in May 2010. It is also running out of money fast.
With an €18bn (£14.4bn) cash injection for the banking system put on hold, a senior official in the outgoing government admitted there were concerns over whether Greece could "make it" until the next election.
"It is a real issue," he told the Guardian. "The economy is in very bad shape. "The banks have no money. There is no liquidity. It is vital that this cash injection is released by the EFSF [the EU's emergency rescue fund]."
EU partners, led by Berlin, have made plain that there can be no further aid without Athens honouring pledges it signed as part of the latest €130bn loan agreement.
The spectre of a fresh ballot will not allay fears. The leftwing Syriza party, the surprise runner-up on 6 May, is expected to emerge first on a platform to "tear up the barbaric accord".
'Syriza' is very close to 'Syria'. Both Greece and Syria are currently defending themselves from invisible forms of warfare at the hands of imperial forces.