- President Karolos Papoulias warns that "things in Greece are quite difficult"
- He will meet with all party leaders on Sunday
- Socialist leader Venizelos says three pro-euro parties may be willing to form a coalition
- The three top-placed parties in Sunday's election have each failed to form a coalition
Athens, Greece (CNN) -- Greek President Karolos Papoulias will hold last-ditch talks with political party leaders Sunday, a week after elections where angry voters punished mainstream parties by backing a range of fringe groups.
He said he hoped he could help form a unity government, adding that "things in Greece are quite difficult."
The leaders of the three biggest parties in the incoming parliament have all tried and failed in the last week to come up with a governing coalition.
Papoulias will meet the leaders of the center-right New Democracy party, the radical leftist Syriza coalition, and the mainstream Socialist PASOK party together on Sunday.
He'll hold talks with the leaders of smaller parties later in the day.
If no government can be cobbled together by May 17, new elections must be called. They would take place next month.
Evangelos Venizelos, leader of PASOK, met the president Saturday after he became the third politician to fail to form a coalition.
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 Syriza, which placed second in last Sunday's election, also joined.
Papoulias described this as a "grain of hope."
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 to 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 last 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 last week'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.
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 last 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.
Journalist Elinda Labropoulou contributed to this report.
