Greek Socialist PASOK leader Evangelos Venizelos meets conservative New Democracy leader Antonis Samaras to try to form a government and avoid a repeat election.
Sunday's election resulted in a hung parliament after fed-up voters punished both the socialists and the conservatives for backing a tough EU/IMF bailout by voting for smaller parties instead.
But officials say the chances of clinching a coalition deal are slim.
If the attempt fails, the Greek president will personally ask all political leaders to make one final effort before new elections are called.