Greek President Karolos Papoulias (R) faces a difficult challenge to unite deeply divided parties
Greek President Karolos Papoulias is preparing to hold talks with party leaders in an attempt to create an emergency government, reports the BBC.
The socialist Pasok party became the third bloc to fail in coalition talks, and leader Evangelos Venizelos formally returned the mandate to the president.
If the president's bid fails, another election will have to be held.
Last Sunday, voters backed parties opposed to Greece's bailout deal that requires deep budget cuts.
Greece's political turmoil has raised the possibility that it could default on its debts and be forced out of the eurozone.
The president is expected to try to pressure parties into a government of national salvation - but the BBC's Mark Lowen in Athens says he is unlikely to succeed.
The process could take days.
Venizelos abandoned efforts to form a new government on Friday, and met the president on Saturday morning to confirm his decision.
He had held talks with centre-right New Democracy leader Antonis Samaras, whose party came first in the election, but could not find a third partner to give them a majority in parliament.
"I hope that during the negotiations chaired by Mr Papoulias everyone will be more mature and responsible in their thinking," Venizelos said.
New Democracy also failed to form a coalition earlier in the week, as did the left-wing bloc Syriza, which came second in the election.
Syriza firmly rejects the terms of the most recent EU-IMF bailout, which requires tough austerity measures in return for loans worth 130bn euros ($170bn; £105bn).
Its leader, Alexis Tsipras, said on Friday he could not join any coalition that intended to implement the bailout deal.
"The rejection of this plan does not come from Syriza but was given by the Greek people on the night of the election," he said.
"The bailout austerity has already been denounced by the Greek people with its vote, and no government has the right to enforce it."
Analysts say Syriza could be hoping for another election after one opinion poll put them in first position in any new ballot, albeit without an overall majority.
Meanwhile Germany has reiterated that Greece's exit from the eurozone would have dire consequences, and urged Athens to continue its deep budget cuts.