Greek President Karolos Papoulias has held talks with leaders of the country's smaller parties on forming a coalition averting new elections.
Consultations earlier in the day with leaders of the three biggest parties failed when Alexis Tsipras, of the radical left Syriza, rejected any deal.
Syriza also clashed with a fourth party seen as a coalition partner.
Parties which agreed to swingeing cuts in return for the last EU/IMF bailout suffered at last week's polls.
Both the centre-right New Democracy and the socialist Pasok have so far been unable to form a new coalition.
Opinion polls suggest the popularity of Syriza, which came second in the election behind New Democracy after running an anti-bailout campaign, has continued to grow.
A new election could make them the biggest party in an anti-bailout coalition, which analysts say could threaten Greece's membership of the euro.
Syriza insists any new government must cancel austerity measures agreed in return for EU-IMF loans worth 130bn euros ($170bn; £105bn).
Mr Papoulias, 82, met individually the leaders of the four other parties that won enough votes for parliamentary seats.
Panos Kammenos, leader of the nationalist Independent Greeks, was the first to see him on Sunday evening at the presidential mansion in Athens, followed by Aleka Papariga of the communist KKE, then Nikolaos Michaloliakos of the far-right Golden Dawn.
The last meeting Mr Papoulias held was with Fotis Kouvelis, leader of Democratic Left, which is seen by some as the only potential coalition partner among the four smaller parties, despite its rejection of austerity.
Mr Kouvelis left the meeting without making any comment.
The BBC's Mark Lowen in Athens says most Greeks appear to be in favour of remaining in the euro, but there are questions as to what sacrifices they are willing to make to achieve that goal.
Mr Tsipras refused to join a proposed national unity coalition with New Democracy and Pasok, saying: "They're not seeking an accord with Syriza... they're asking us to be their partners in crime and we will not be their accomplices."
A row erupted after he accused Democratic Left of agreeing to form a coalition with New Democracy and Pasok.
Democratic Left, which has been asking for Syriza to be included in any new coalition, denied any such agreement. On its website, the party accused the Syriza leader of a "slander and a lie".
Mr Kouvelis said before Sunday's talks that any coalition government should "immediately" cancel legislation that slashed the minimum wage and facilitated lay-offs, and start to "disengage" Greece from the bailout.
"I harbour doubts on whether a deal will emerge... I have very little hope," he was quoted as saying by AFP news agency.
The leader of New Democracy, Antonis Samaras, said Syriza had refused to join or back a coalition government, even if it pledged to "renegotiate" the loan agreement.
"Syriza not only refuses to accept the formation of a viable government but also to give a vote of tolerance to a government that would renegotiate the terms of the loan agreement," he said.
If, as expected, the talks fail to produce a governing coalition, a new election will be scheduled for next month.
The uncertainty has alarmed Greece's international creditors, who insist the country must keep to the terms of the bailout deal if it is to continue receiving funds and avoid bankruptcy.
Correspondents say the anti-bailout vote that was shared among several small parties in the first election now seems to be consolidating around Syriza.
Several opinion polls have put Syriza - runners up to New Democracy in last Sunday's election - in first place in any future poll.
With a bonus of 50 extra parliamentary seats that winning would bring, an anti-bailout coalition led by Syriza is looking more likely.
Mr Tsipras insists he wants to keep Greece in the euro, and says European leaders are bluffing when they threaten to eject Athens from the single currency if it reneges on bailout agreements.
Greece's socialist daily newspaper, Ethnos, warned on its Sunday front page that politicians were playing "Russian roulette" with the country's damaged economy, in its fifth year of recession.