Greek moderate Democratic Left party says it will not join pro-bailout parties in a coalition without the more radical far left Syriza.
The Greek president has called the four main parties, including the centre-right New Democracy and the Socialist Pasok, to try to form an emergency government to avoid new elections.
But Syriza said it would not attend because it could not back any coalition which supported austerity.
A majority voted against last week.
EU finance ministers are due to meet in Brussels to discuss the Greek crisis later on Monday.
The fear over holding new elections is that parties that oppose austerity measures that are a condition of Greece’s bailout deal might do well again in new polls.
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.