Athens, Greece (CNN) -- Greek President Karolos Papoulias is to hold talks in the next day with party leaders in a bid to create a national unity government, his office said Saturday.
Evangelos Venizelos, leader of the country's socialist party, PASOK, met with the president Saturday after it became the third party to fail to form a coalition, a week after parliamentary elections gave no one a majority.
Speaking after the meeting, Venizelos said PASOK, New Democracy and the Democratic Left have said they would be willing to go into a grand coalition on the condition of remaining in the euro, offering a possible way out of the impasse.
But this could still be problematic as the Democratic Left has previously said it will only join a coalition if the party which placed second in Sunday's election, the Coalition of the Radical Left, or Syriza, also joined.
Papoulias described this as a "grain of hope."
He said he hoped he could help form a unity government, adding that "things in Greece are quite difficult."
Papoulias is expected to meet with the leaders of PASOK, New Democracy and Syriza at noon Sunday, his office said. He will meet with other party leaders later.
If the president's bid to form a unity government does not succeed by May 17, fresh elections must be called. They would take place next month.
Deep uncertainty surrounds the political situation in Greece after large numbers of voters in last Sunday's election backed parties opposed to the country's bailout deal.
Severe austerity measures are required under the terms of the bailout, agreed by the outgoing coalition government of PASOK and New Democracy.
Headlines in Saturday's papers talk about "Elections on the Titanic" and "Opening the door to an exit from the euro."
A poll earlier this week suggested that if new elections are held, Syriza would come first with 28% of the vote, although without achieving a majority. Syriza came in second in Sunday's election with 16.8%.
The party is opposed to the terms of the bailout agreed with the European Union, European Central Bank and International Monetary Fund, and has even suggested implementing a moratorium on part of the repayments.
The country's lenders have said that if Greece does not comply with the bailout terms then payments will stop.
Greece has been forced to impose punishing austerity measures to get international loans that have kept it from defaulting on debts so far.
But this week's election results were widely seen as a message to politicians to back away from the economic measures, which include policies to cut spending and raise taxes to reduce public debts.
Seven parties won seats in parliament, but none captured more than 19% of the vote, leading to a week of political turmoil.
The stakes are potentially huge for the rest of the eurozone, the group of 17 European countries that use the euro as single currency.
There is concern that the lack of leadership could jeopardize Greece's bailout agreement. That could lead to a disorderly default by Greece, which would force the nation out of the eurozone.
A default by Greece also could drag down other troubled governments such as Spain and Portugal. The eurozone economy is fragile, and any financial shock could plunge the region into a deep recession, a development that would ripple across the globe.