Negotiations on forming a new Greek government have ended after an hour but will resume on Tuesday.
Three previous attempts to form a government have failed. If the parties cannot agree on a coalition, new elections must take place next month.
The left-wing Syriza bloc - the second largest in parliament - did not attend the talks, saying it would not join any coalition making further cuts.
Syriza rejects the terms of the EU/IMF bailout, which demand more austerity.
"Things are very difficult. I'm not optimistic," said Evangelos Venizelos, leader of the Socialist Pasok party, after the talks, according to the Reuters news agency.
A majority of Greek voters backed parties opposed to the austerity needed to meet the terms of the 130bn euro ($170bn; £105bn) bailout agreed with the EU and International Monetary Fund (IMF).
European markets and the euro fell sharply on Monday. The euro stood at $1.2845, down 0.54% from Friday.
The leaders of the centre-right New Democracy, Pasok and moderate Democratic Left parties arrived at the presidential palace shortly after 19:30 (16:30 GMT) on Monday for talks.
They left an hour later. President Karolos Papoulias called another round of talks for Tuesday, to include all parties except the far right.
Mr Papoulias has proposed a technocratic government.
Syriza's leader Alexis Tsipras rejected the invitation from the Greek president to join the coalition talks on Monday, saying he would not be a party to what he called a crime.
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