Greek conservative leader Antonis Samaras says he has failed to form a coalition government and has handed back the mandate to President Karolos Papoulias.
Mr Samaras, whose New Democracy party won the biggest share of the vote in Sunday's inconclusive election, was given the first chance to form an administration by the president.
Syriza, which took second place, will now be given the opportunity to try and form an administration.
President Papoulias has arranged a meeting for Tuesday morning with Syriza leader Alexis Tsipras.
Mr Tsipras will have three days to negotiate a coalition.
New Democracy will still be the largest party in the new parliament.
Mr Samaras says the party did everything it could but it was impossible to form a government in the current political environment.
Two-thirds of Greek voters backed parties opposed to the EU/IMF deal, renewing fears that Athens may default on its debts and leave the eurozone.
Chancellor Angela Merkel of Germany has made clear that Greece's reforms must go on, saying they are of ''utmost importance''.
A further 11 billion euros of cuts in spending is due to be found next month under Greece's current bailout plan.
Since November, Greece has been run by a coalition, led by technocrat Prime Minister Lucas Papademos, which secured a 130 billion euro deal this year.
Pasok was in power when Greece negotiated the terms of a bailout of 110 billion euros in 2010.
New Democracy's support on Sunday slipped from 33.5% to less than 19% of the vote while Pasok's share plummeted from 43% to just over 13%.
If Syriza fails to form a coalition, Pasok, the third party will receive the mandate. If still no coalition emerges, Greece will hold another election.
Syriza is opposed to the austerity measures.
Pasok's leader, former finance minister Evangelos Venizelos, has called for a broad coalition government of pro-European parties.
''A coalition government of the old two-party system would not have sufficient legitimacy or sufficient domestic and international credibility if it would gather a slim majority,'' he said on Sunday.