Greece's radical left party, Syriza, will try to form a unity government after mainstream conservatives failed to cobble together a coalition.
The head of Greece's conservative New Democracy party, Antonis Samaras, announced Monday he was unable to form a coalition government after rejections from several party leaders.
The New Democracy party won the most votes in Sunday's election and was therefore given the first chance to form an administration. Now, President Karolos Papoulias is giving Syriza's Alexis Tsipras three days to put together a ruling alliance.
If those talks fail, the party that came in third will get the mandate to try to gain a majority in the 300-seat parliament.
No agreement could force new elections next month.
Syriza rejects European Union austerity measures imposed on the debt-laden country.
Nervous European leaders have maintained pressure on Greece to continue respecting the requirements imposed on Athens in return for more than $300 billion in two bailouts.
The bailout deal, struck in February with the European Union, the International Monetary Fund and the European Central Bank, aims to clear the way for Greece to return to financial markets by 2015.
Some information for this report was provided by AFP and Reuters.