In the meeting, Papoulias said the New Democracy party, which has supported him, had two conditions: to ensure that the country remains in the euro and to renegotiate conditions of the bailout.
In a poll published Saturday by the newspaper Kathimerini, four of five voters said they would vote the same way in a new election.
In a separate poll published Sunday by the newspaper Vima, seven 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 of 10 voters said Syriza's plans against austerity are not realistic.
Syriza is opposed to the terms of the bailout agreed to 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.
The stakes are potentially huge, with concern stirring that the lack of leadership could jeopardize Greece's bailout agreement. That could lead to a disorderly default by Greece and force the nation out of the eurozone.
A default by Greece also could drag down other troubled governments such as Spain and Portugal. Any financial shock of such a magnitude could plunge the region into a deep recession, with ripples being felt across the world.