The leader of Greece's left-wing Syriza bloc has urged the country's two biggest parties to abandon their commitment to austerity.
Alexis Tsipras has been given three days to try to form a coalition government after his mainstream rivals failed to agree to a deal in the wake of Sunday's election.
Mr Tsipras says Greek voters have rejected the bailout agreed with the European Union and the International Monetary Fund, which he describes as "barbaric".
On Wednesday, he will meet the two mainstream pro-bailout parties, Pasok and New Democracy (ND).
If the two sides fail to agree, Greece could face fresh elections in weeks.
Mr Tsipras wants a government that turns its back on cost-cutting and Greece's bailout commitments.
He secured agreement from one centre-left party on Tuesday.
But a BBC correspondent reports that the party leaders who signed the bailout deal are unlikely to agree to his terms.
If no deal is reached, a perilous power vacuum would be created, the correspondent says.
Greece would be unable to draw its international loan, meaning it would again face the prospect of bankruptcy and possible exit from the euro, he adds.