Communist party leader Aleka Papariga, who addressed thousands of supporters at an Athens rally Monday, said she would not attend the new talks.
Democratic Left leader Fotis Kouvelis said after Monday's meeting that he was "categorically" against a government of technocrats or respected personalities, adding: "That would be a defeat for politics."
With the left apparently out of the picture, a potential breakthrough could come from the right. An hour before Tuesday's meeting, Papoulias will separately see Panos Kammenos, head of the new Independent Greeks party that garnered 10.6 percent of the vote on May 6.
Samaras said there was "some margin" for Kammenos to back a power-sharing deal.
But political analyst George Sefertzis warned that leaving the left out of government could create more problems than it solved.
"It would be better to have new elections ... rather than seek a hasty way out that will have the disadvantage of creating an opposition strengthened by the non-inclusion of the left," he said.
Left-wing support seems to be growing as new elections appear ever likelier. In a poll published Monday, the Radical Left Coalition had 20.5 percent of public support, compared with 19.4 percent for New Democracy and 11.8 percent for PASOK. The margin of error was 3.1 percent for the Rass poll of 1,002 people, conducted May 10-11 for the Eleftheros Typos newspaper.
Sefertzis said holding a new election would be "playing with fire" since the delay would further complicate Greece's financial situation. But he said that a new popular mandate clearly backing a coalition government might force the issue.
Opinion polls have shown that most Greeks want a power-sharing deal.
"I believe that a way must be found for all the political parties to find some common ground of communication, to agree at least on what they consider is necessary for survival of this country," Athens IT technician Andreas Chrisitakis said.
Elena Becatoros and Derek Gatopoulos contributed.
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