Greece starts a second day of coalition talks on Tuesday under the gun from financial markets and world powers after elections won by pro-euro parties that also reflected rising anger against austerity.
The New Democracy conservatives who came first in the elections said they had struck a preliminary agreement with the socialists Pasok to form "a government of national salvation" to rescue Greece from its devastating economic crisis.
Pasok has voiced hope for a deal later on Tuesday but insists that the new government should include other parties including the radical leftist Syriza, which has already ruled out taking part in any New Democracy-led coalition.
Europe and the United States have urged Greece to move quickly to form a new government and enact reforms under the terms of a controversial multi-billion bailout deal with the European Union and the International Monetary Fund.
"The country cannot remain ungoverned even for an hour," Greek President Carolos Papoulias said on Monday, as he gave a three-day mandate to form a coalition to New Democracy's Harvard-educated leader Antonis Samaras.
World stock markets initially rallied in reaction to Sunday's elections and the euro rose sharply against the dollar but the gains quickly petered out amid broader concerns about other indebted euro economies like Italy and Spain.
Syriza, which has called for the EU-IMF bailout deal to be scrapped and renegotiated from scratch, won more than a quarter of the vote in Greece's most important elections since the end of military rule in 1974.
Samaras's conservatives won 129 of the 300 parliamentary seats, Syriza won 71 seats and Pasok 33 seats. The small Democratic Left party, a pro-European movement seen as a possible coalition partner with New Democracy, won 17 seats.
In a reflection of widespread concern about security and immigration in a fifth year of recession for Greece, the neo-Nazi Golden Dawn party also won 18 seats depite a number of high-profile assaults involving its candidates.
Analyst Yiannis Loulis warned that any new government would be a "fragile" one and some analysts warn that even with pro-bailout parties in power there is potential for a confrontation with Greece's international creditors.
Samaras has promised to respect Greece's international engagements but also said on Monday that there should be amendments to the harsh conditions of the bailout deal "so the Greek people can escape from today's torturous reality".
Key EU player Germany has said there could be an extension of a deficit deadline but New Democracy's campaign promises appear to go further, including a reduction in property and sales taxes and a freeze in pension and salary cuts.
"Elections cannot call into question the commitments Greece made. We cannot compromise on the reform steps we agreed on," German Chancellor Angela Merkel warned in Mexico at the G20 summit on Monday.
Also at that summit US President Barack Obama said the election result was a "positive" sign for Greece to work "constructively with their international partners in order that they can continue on the path of reform."
Greece has been forced to seek bailouts twice after hiding the extent of its debt woes, first for 110 billion euros in 2010 and then for 130 billion euros earlier this year. It has also had a 107-billion-euro private debt write-off.
The eurozone is hoping the result can draw a line under a lengthy period of uncertainty that has unsettled markets in a country where the sovereign debt crisis kicked off in 2009 before spreading across the continent.
Any new government faces daunting economic challenges in a country where unemployment is at 22.6 percent, with a tricky political balancing act between pressure from the streets and from the global financial community.