The moderate Democratic Left party in Greece says it will not join pro-bailout parties in a coalition without the more radical far left Syriza.
But Syriza said it would not attend because it could not back any coalition which supported austerity.
Greece was plunged into further political disarray with the refusal of Syriza to join talks on forming a government of national unity.
The move takes the country a step closer to elections, which polls now suggest the anti-bailout party could win.
Earlier leaders of Greece's three largest political parties ignored a final plea from the president to form a coalition government to avert a repeat election, pushing the debt-stricken nation closer to bankruptcy and a possible exit from the euro zone.
The party leaders met on Sunday at the presidential mansion for a final attempt to bridge their differences, but the talks quickly hit an impasse over the international bailout package which is tied to harsh spending cuts.
Antonis Samaras, whose conservative New Democracy finished first in the election on 6 May, is pinning the blame on the far-left Syrzia party, which flatly rules out backing a pro-bailout coalition with the other two parties, Reuters reports.
Alexis Tsipras, who led Syriza to a surprise second place in the vote, says the other two parties are asking it to be their partners in crime and "we will not be their accomplices."
The leader of the Socialist Pakok party, Evangelos Venizelos, says he is holding on to hopes a deal can still be salvaged, but time is running out.
Greek president Karolos Papoulias will hold negotiations with smaller parties. His final hope rests with the small Democratic Left party led by lawyer Fotis Kouvelis, which could provide enough seats to form a government with New Democracy and Pasok. But it says it will not do so unless the coalition also includes Syriza.
Both New Democracy and Pasok - which have taken turns in ruling Greece for nearly four decades and jointly negotiated a bailout that requires deep cuts in wages, pensions and spending - are eager to avoid facing voters again.
Polls since the election show the balance of power tipping even further towards opponents of the bailout, who were divided among several small parties but now appear to be rallying behind Mr Tsipras, a 37-year-old ex-Communist student leader.
Mr Tsipras has promised to rip up the bailout deal without abandoning the euro, saying Europe cannot afford to cut Greece loose.
But European leaders warn Greece will not get new loans to stay afloat if it fails to honour its pledges, while banks and some companies have begun to prepare for a Greek exit from the eurozone.