Hopes have risen slightly that Greece can end its post-electoral deadlock without having to hold new elections, as international partners warned that Athens must stick to its austerity programme or abandon the euro.
Socialist leader Evangelos Venizelos, who received the presidential mandate to try to form a government after two other party chiefs failed, said a meeting with a left-wing potential kingmaker had proved encouraging.
If this third mandate fails, President Karolos Papoulias will convene party leaders in a last-ditch effort to get a deal - otherwise new elections will be held in a month.
New elections would greatly delay Greece's commitments to pass further austerity measures and reforms, without which creditors will cut off the country's rescue loan lifeline. If Greece runs out of cash, it could be forced to leave the euro, reverting to a grossly devalued version of its old drachma currency.
Mr Venizelos, whose once-dominant PASOK party finished third in Sunday's elections, said he and pro-European Democratic Left leader Fotis Kouvelis were "very, very close in our views".
The leftist Mr Kouvelis wants a broad coalition to keep Greece in the euro and "launch a gradual disengagement" from the austerity programme with a mandate until mid-2014. Mr Venizelos said that "almost coincides" with his own position.
Voters angered by crushing income cuts imposed to secure Greece's rescue loans abandoned mainstream politicians on Sunday and backed parties promising to end the belt-tightening. They even gave 21 seats to the extreme-right Golden Dawn, which wants to send illegal immigrants to labour camps.
The coalition-building talks exclude Golden Dawn, but the other six parties elected have failed to come up with a working government over the past four days.
If Mr Kouvelis' party joined with PASOK and first-placed conservative New Democracy party - both of which have pledged to respect their pre-election commitments for protracted austerity - their coalition would control 168 of Parliament's 300 seats.
But the situation remains highly volatile, as Mr Kouvelis would risk being branded as a left-wing traitor if he helps the pro-austerity parties to govern without the second-paced Radical Left Coalition, which is staunchly anti-bailout.
Mr Venizelos is the third party leader to try, after Antonis Samaras, whose conservative New Democracy won the most votes, and the Radical Left's Alexis Tsipras. He has three days to strike a deal.
The major stumbling block has been Mr Tsipras' insistence that the austerity programme be cancelled or frozen. Both Mr Samaras and Mr Venizelos argue such a move would be catastrophic for the country, and would force Greece out of the euro.
In a letter to European leaders today, Mr Tsipras said the election result left Greece's bailout commitments devoid of "political legitimacy," but stopped short of demanding that the programme should be scrapped and debt repayments halted.
Mr Tsipras said the cutbacks have failed to address the country's problems, are "destroying" the recession-bound economy and threatening to create a Greek "humanitarian crisis."
But German finance minister Wolfgang Schaeuble said Greece must stick to its austerity measures if it wants to stay inside the eurozone. He categorically ruled out any renegotiation of the agreements, saying calls to do so did not chime with the current economic reality.
"Anyone who tells Greece something else isn't fulfilling their duty to the Greek people," he said.
Athens has promised to pass new austerity measures next month and to implement other reforms. These will be reviewed by its creditors - the International Monetary Fund and other eurozone countries - who will then determine whether to continue releasing the rescue loans that are keeping Greece solvent.