Greece's third-placed socialist Pasok party failed to form a coalition government on Friday night.
Another round of parliamentary election is likely since none of the major parties were able to form a stable government.
"I am going to inform the president of the republic [Saturday] and I hope that during the meeting with Carolos Papoulias, each party will assume its responsibilities," said socialist leader Evangelos Venizelos after his unsuccessful attempt, reported AFP.
Venizelos becomes the third party leader who did not succeed in forming the government after the New Democracy and Syriza parties.
Venizelos is expected to hand over the mandate back to the president on Saturday.
There will be a last attempt by the president on Saturday to bring a consensus between the parties to form a coalition which is likely to prove futile.
The country has been deeply divided over the budget cuts which are being demanded by the EU and the IMF in return for their bailout worth around 240 billion euros.
Reacting to Pasok's inconclusive talks, Syriza's leader Alexis Tsipras said: "It is not the left coalition that has refused this proposal, but the Greek people who did so with their vote on Sunday," quoted Reuters.
Two major parties, the New Democracy and Pasok, were defeated in last Sunday's elections in which both did not secure a majority leading to the current political crisis.
Political analysts and opinion polls are predicting a bigger victory for the Syriza parties if fresh elections are held in the middle of June.
"I think it is going to be increasingly presented as a vote to effectively leave the euro. That's how it will be seen outside of Greece and the rhetoric will build up to ensure that voters are aware of the implications," Reuters quoted Markit' Chief Economist Chris Williamson as saying.
"We're likely to hear: if you want to stay in Europe you need to stick to our rules; you can't have a situation whereby you escape the obligations with regards to debt and remain in our area," Williamson added.
Likelihood of the country's expulsion from the single currency EU bloc is equally haunting. The scenario seems much more likely given the political turmoil over the past few weeks.
The BBC quoted German Foreign Minister Guido Westerwelle as saying: "The future of Greece in the eurozone lies in the hands of Greece.
e want to and we will help Greece, but Greece has to be ready to accept help. If Greece strays from the agreed reform path, then the payment of further aid tranches won't be possible. Solidarity is not a one-way street."