Greek President Karolos Papoulias will make on Sunday a final push for the formation of a coalition government following the May 6 national polls that gave no party parliamentary majority, the president's office said on Saturday.

The statement came after Papoulias met with socialist PASOK party leader Evangelos Venizelos who returned the exploratory mandate he had been given on Thursday.

According to the statement, Papoulias will hold a series of meetings with leaders of all seven parties that enter the new assembly, according to the constitution.

The president will receive first the three party chiefs that held the mandate in their hands over the past week, trying to form a national unity administration.

They include Antonis Samaras of conservative New Democracy (ND), Alexis Tsipras of the radical leftist SYRIZA coalition and Venizelos. Their parties ranked first, second and third in Sunday's elections.

During Saturday's meeting, Venizelos told Papoulias that PASOK, ND and the smaller Democratic Left party that ranked last in the elections agree on a pro-European interim government with a two-year term to keep Greece in the eurozone and renegotiate some terms of the bailout contracts with international lenders to overcome the severe debt crisis.

He implied that efforts should focus on persuading SYRIZA to join a coalition.

But Tsipras retains a hard line against austerity imposed under the deals signed with other EU countries and the International Monetary Fund since 2010 in exchange of multi-billion euro loans to avoid a Greek default. SYRIZA asks for a drastic review of some tough austerity measures that have made life hard for recession-hit Greeks.

Papoulias expressed hope that his contribution in efforts to set up a government will be positive, as "things are very difficult."

Local and foreign officials and analysts warn that if Greece misses timetables and goals under the bailout agreements amidst political instability, lenders could stop releasing the next tranches of aid and the country would face bankruptcy and a possible exit from the eurozone.

The Greek constitution does not set a time frame for deliberations under auspices of the president. If this last bid fails, the constitution gives Papoulias the option of appointing a caretaker government headed by the presidents of the Supreme Court or Council of State, before calling new elections when the new parliament convenes on May 17.

According to Greek media reports, a second round of polls could take place on June 10 or June 17.