Greek President Karolos Papoulias has called the country's leaders to a meeting on Sunday in a last-ditch attempt to forge a unity government.
If the president's bid fails, another election will have to be held.
Earlier, Pasok became the third party to fail in coalition talks when leader Evangelos Venizelos formally returned the mandate to the president.
Last Sunday, voters backed parties opposed to Greece's bailout deal, which 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.
Mr Papoulias said in a statement he would hold a meeting at 09:00 GMT on Sunday with the leaders of the three largest parties - the socialist Pasok, the centre-right New Democracy, and far-left bloc Syriza.
He will then hold talks with fringe parties including Golden Dawn, an extreme right-wing anti-immigration group.
Analysts say the president's bid is unlikely to succeed because the parties are so divided over the bailout.
Mr 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 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," Mr Venizelos said.
New Democracy also failed to form a coalition earlier in the week, as did 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 bailout austerity has already been denounced by the Greek people with its vote, and no government has the right to enforce it," he said.
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.
"For Greece the consequences would be much more grave than for the rest of the eurozone," said Jens Weidmann, head of Germany's central bank.
The Bundesbank chief told the Sueddeutsche Zeitung newspaper that Greece must continue its austerity reforms to justify further loans from the international community.
"If Athens does not stand by its word, then that's a democratic decision. The result is that there is no more basis for further financial aid," he said.
Sunday's election saw a backlash against Pasok and New Democracy, the two parties that agreed the terms of the latest bailout.
The once-dominant Pasok, which was seen as the architect of austerity, came third with just 41 seats in the 300-seat parliament.
The Greek crisis is continuing to create unease is global financial circles.
The Fitch ratings agency warned that if Greece did leave the euro, it would probably place all 16 remaining euro nations' sovereign ratings on "rating watch negative" - meaning they would be in danger of being downgraded.
"A Greek exit would break a fundamental tenet underpinning the euro - that membership of EMU [Economic and Monetary Union] is irrevocable," Fitch said.