Leaders from all bar the far-right parties that won seats in inconclusive 6 May polls will meet at on Tuesday to try and get the country "out of a dead end", Socialist Pasok party head Evangelos Venizelos said on Monday.
Time is tight - parliament convenes on Thursday and if no government is in place, new polls will have to be called, prolonging an agonising crisis by another month to the dismay of Greece's EU partners and the markets.
President Carolos Papoulias met Venizelos and heads of the conservative New Democracy and radical Democratic Left, proposing on Monday in the absence of any other solution a government of "distinguished and non-political figures".
"I think time is against us," Papoulias told the meeting, adding: "I am terrified at the idea of the problems facing the country" in the coming days.
A first test comes on Tuesday with a government bond sale, which will be closely watched after European financial markets tumbled on Monday at the prospect that the eurozone debt crisis could now snag troubled Spain or even Italy.
Leaving the euro
The markets rebounded slightly on Tuesday as investors welcomed news that Germany avoided recession in the first quarter of the year, with London's benchmark FTSE 100 index gaining 0.33% to 5 483.72 points.
In the 6 May polls, Greek voters roundly rejected the tough austerity measures the outgoing technocrat government of Lucas Papademos agreed to in return for the €240bn EU-IMF bailout accord.
Picking up on a groundswell of opposition across Europe to governments that put austerity before growth, both left and right gained at the expense of New Democracy and Pasok, which had supported Papademos to get the debt deal done.
In recent months senior officials have more openly raised the prospect of Greece leaving the euro, but on Monday the head of eurozone finance ministers group hit back strongly, insisting that Athens was staying put.
"I don't envisage, not even for one second, Greece leaving," Jean-Claude Juncker said after the 17 eurozone partners unanimously affirmed their "unshakable desire" to keep Greece in the club.
"This is nonsense, this is propaganda," he said, adding that the Eurogroup "will do everything possible" to prevent a Greek exit and that "absolutely no one argued in that direction".
Opposition to technocrat solution
There can be little doubt about the seriousness of the situation.
Charles Dallara, who as head of the Institute of International Finance helped negotiate a massive private creditor bond write-down for Greece as part of the EU-IMF bailout, warned that the cost of failure would be too high.
"I believe that the cost to Greece, the cost to Europe and the cost to the entire global economy may still be enough to cause Greek politicians and European politicians to pause before they pull the trigger on a Greek exit."
New Democracy leader Antonis Samaras said on Monday after the announcement of Tuesday's talks that "everyone must take their responsibilities. ... Our mandate all together is to build a government".
Democratic Left head Fotis Kouvelis, who had earlier on Monday said there was no chance of a deal if the radical left Syriza party was not included, indicated that he would go to Tuesday's meeting but poured cold water on the technocrat option.
"I told the president ... that a government formed by technocrats and personalities means the defeat of politics. ... I expressed the view that I am against it," he said.
Wants it both ways
For Greeks, the situation is both difficult and confusing.
Many want to remain in the eurozone for the benefits it brings but strongly oppose the tough EU-IMF austerity measures as the country languishes in recession for a fifth year.
Greece wants it both ways, "to remain in the eurozone but not have the loan agreement", said unemployed Velisarios.
"That is what the majority wants ... [but] of course, something like that can't happen."