Greek President Karolos Papoulias is to make a last attempt to persuade some political parties to form an emergency government to avoid new polls.
One of the four parties invited for talks, the far-left group Syriza, has said it will not attend.
This leaves the centre-right New Democracy, the Socialist Party (Pasok) and the moderate Democratic Left as possible coalition partners.
EU finance ministers will meet in Brussels to discuss the Greek crisis.
The leader of far-left party Syriza will not attend coalition talks on Monday, plunging Greece into further political disarray.
The move by Alexis Tsipras takes the country a step closer to elections.
The fear is that parties that oppose austerity measures that are a condition of Greece's bailout deal might do well again in new polls, says the BBC's Gavin Hewitt in Brussels.
And with no sign Europe's leaders are prepared to renegotiate the deal, Greece could end up leaving the eurozone.
For the first time, some central bankers have spoken openly about the consequences of a Greek exit from the single currency, our correspondent adds.
President Papoulias had invited four parties, including Syriza, to further talks.
Both New Democracy and Pasok have so far been unable to form a new coalition.
They both agreed to swingeing cuts in return for the last EU/IMF bailout, but suffered at last week's polls.
Syriza, which came second, insists any new government must cancel austerity measures agreed in return for EU-IMF loans worth 130bn euros ($170bn; £105bn).
Leading European figures, including European Commission head Jose Manuel Barroso, have warned that Greece must respect the terms of the bailout deal if it wants to remain in the euro.
Officials are weighing up the fallout of a potential Greek withdrawal from the euro and how that would be managed, say analysts.
In theory, Democratic Left - which came seventh in the election, winning 19 seats - could provide New Democracy and Pasok with the support needed to form a coalition, but its leader, Fotis Kouvelis, has repeatedly said he would not do so without Syriza.
It became clear that Mr Papoulias's consultations with party leaders on Sunday were likely to be fruitless when 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 Mr Tsipras accused Democratic Left of agreeing to form a coalition with New Democracy and Pasok - an accusation that Democratic Left rejected as a "slander and a lie" on its website.
Emerging after the talks, Mr Kouvelis said the president had told him there was "no possibility of the formation of a unity government, and he referred to the refusal by Syriza to participate in such a government, or to even show tolerance towards one".
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.
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.
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 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.