Greece's centre-left leader Evangelos Venizelos has met the country's president about the possibility of forming a coalition government following last Sunday's inconclusive election.
Mr Venizelos has three days to form a government, but few analysts believe that he will be successful.
He is the third leader to attempt to form a government since weekend polls delivered a strong message against austerity.
New Democracy leader Antonis Samaras failed when given the first opportunity to form a coalition.
Alexis Tsipras, a radical leftist, had been given until today to form a government.
Greeks who voted overwhelmingly to reject parties behind an EU/IMF bailout say they are ready to do it all over again if, as seems all but certain, the election is rerun.
Politicians show little sign of being able to cobble together a government, which means a new election is likely to be held in three to four weeks.
The political disarray has fuelled speculation Greece could be ejected from Europe's single currency, even though polls show most Greeks want to keep the euro.
The conservative New Democracy and Socialist PASOK have alternated ruling Greece since the fall of the military junta in 1974.
Last year, with bankruptcy just weeks away, they formed a coalition and jointly negotiated the €130bn EU/IMF bailout.
But the two parties that dominated Greece for decades were reduced to just 32% of the vote at the weekend.
EU leaders have made clear since Sunday that Greece must stick to the reforms agreed in return for the bailout - including firing public sector workers, slashing pay and raising taxes - to keep getting aid and stay in the euro.
Greeks say they want a rescue plan that would not hurt the poorest and middle class as much.
Many Greeks said they wanted to see a swift coalition and blamed the politicians for causing chaos by stalling.