ATHENS, Greece (CNN) -- The Greek president will try again Monday to get political leaders to form a new government for the troubled country, but as the clock ticks down, the head of the second-largest party said he would not attend.
Alexis Tsipras said he was willing to meet one-on-one with President Karolos Papoulias or with all party leaders except the far-right Golden Dawn group, but refused to join "selective discussions."
His radical leftist Syriza group came in second in parliamentary elections on May 6, and opinion polling since then suggests it would come in first if the politicians have to call new elections because they cannot form a government.
The debt-racked country has until Thursday to come up with a government or call new elections.
If Greece is left without a government for that long, it could run out of money to pay its debts and might crash out of the euro, the currency used by 17 European Union countries.
"If no government is in place before June when the next installment (of loan money) from the European Union and International Monetary Fund is due, we estimate that Greece will run out of money sometime between the end of June and beginning of July , at which point a return to the drachma would seem inevitable," Bank of America/Merrill Lynch wrote in a report released Friday.
The Syriza party that Tsipras leads campaigned against the tough restrictions on government spending, which international lenders imposed in exchange for their financial backing.
Tsipras said Sunday that other parties wanted Syriza to be their "partners in crime," adding: "We can't do that."
Papoulias had called together the leaders of the three biggest parties, a week after indecisive elections and three failed attempts to form a government.
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.
After the meeting, 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' remarks "a disgrace," accusing him of lying and slandering the smaller party.
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 that 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."
Tsipras said other parties could form a government without his support.
"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 it was ready for new elections if necessary.
Antonis Samaras, the leader of the center-right New Democracy party, said before the meeting Sunday that voters had called for collaboration, change and staying within the eurozone, the group of 17 European countries that use the euro as single currency.
The Communist party, meanwhile, called for new elections, saying it 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 in first if new elections were held, the Vima poll suggested, after coming in second behind New Democracy a week ago with 16.8% of the vote. 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 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.
Seven parties won seats in parliament, but none captured more than 19% of the vote, leading to the current political turmoil.
The stakes are potentially huge for the rest of the eurozone. 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.