Athens, Greece (CNN) -- The Greek president will resume talks Monday with political party leaders in a scramble to try to form a new government.
President Karolos Papoulias called together the leaders of the three biggest parties Sunday, a week after indecisive elections and three failed attempts to form a government raised the possibility of new elections in the debt-stricken country.
After the meeting, the leader of the radical leftist Syriza coalition said other parties wanted Syriza to be their "partners in crime," adding: "We can't do that."
Syriza leader Alexis Tsipras suggested the two other largest parties, New Democracy and PASOK, were going to form a coalition with a smaller group, the Democratic Left.
But the Democratic Left issued a statement calling Tsipras's remarks "a disgrace," accusing him of lying and slandering the smaller party.
Europe is keeping a nervous eye on Greece, fearing that the political chaos there could lead to defaults on debt that could threaten the future of the euro. Greek failure -- or refusal -- to make debt payments could hurt banks across Europe.
The talks with Papoulias came a week after elections in which angry voters punished mainstream parties by backing a range of fringe groups.
Democratic Left leader Fotis Kouvelis held his own meeting with Papoulias late Sunday. So did Nikolaos Michaloliakos, the head of the far-right Golden Dawn party. Michaloliakos emerged from talks saying any new government would need an internationally respected premier with the clout to reject the bailout package the previous government signed, calling the deal "a crime against our country."
If no government can be cobbled together by Thursday, new elections must be called. They would take place next month. Papoulias said he hoped he could help form a unity government, adding that "things in Greece are quite difficult" -- but things only looked more difficult after Sunday's talks.
Tsipras, whose party came in second last week on a platform of rejecting the conditions that international lenders have placed on the country, said that New Democracy, PASOK and the Democratic Left could form a majority government without the backing of his party.
Polls suggest that Syriza, which came second in voting last week, would come first, if another round of elections is held.
"The three parties have 168 seats together. They can go ahead with that. They are pressuring us to participate, and that is an irrational and unprecedented request. They want us to give a fake sense of legalization," he said.
But the Democratic Left said it had not agreed to back a coalition without Syriza and said of Tsipras: "His obvious inability to justify his stance should not lead him to slander and lie. This is an unethical political act on his part."
Evangelos Venizelos, leader of the Socialist party PASOK, said after the meeting that his party would do everything possible to form a national unity government, but that they were ready for new elections if necessary.
Venizelos had gone to Papoulias on Saturday to admit he could not form a government, making him the third politician in a week to fail to form a coalition.
Antonis Samaras, the leader of the center-right New Democracy party, said before the meeting on Sunday that the voters had called for collaboration, change, and staying within the eurozone, the group of 17 European countries that use a common currency.
Papoulias met Samaras, Venizelos and Tsipras together on Sunday.
Independent Greek Party leader Panos Kammenos complained about the way Papoulias was organizing the meetings, saying all party leaders should meet together.
The Communist party, meanwhile, called for new elections, saying they will not participate in a coalition government.
Four out of five voters said they would vote the same way in a new election, according to a poll published Saturday by the newspaper Kathimerini.
In a separate poll published Sunday by the newspaper Vima, seven out of 10 people said they wanted the parties to form a coalition government.
Syriza would come top if new elections were held, the Vima poll suggested, after coming in second behind New Democracy a week ago. But the results would still lead to a deeply divided parliament, the poll suggested, with no party getting more than 21% of the vote.
In the same poll, six out of 10 voters said Syriza's plans were not realistic. Party leader Tsipras made a radical speech last week against austerity.
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, payments will stop.
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."
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.