Leader of Greece's radical leftist SYRIZA coalition Alexis Tsipras received on Tuesday a "historic" mandate to form a coalition government to lead the country on an anti-austerity, anti-bailout agenda.

He is the second party leader that has been handed the three-day exploratory mandate by Greek President Karolos Papoulias in accordance with the constitution.

Sunday's national polls gave no party parliamentary majority, showing the way to a coalition administration or a second round of elections in June.

Antonis Samaras, leader of conservative New Democracy party that topped the polls with about 19 percent of votes and 108 seats in the new 300-member strong legislature, returned the mandate on Monday night, after failing to win over coalition partners during talks with other party leaders.

"It is a historic moment for the left. We intend to do our best," Tsipras said during his visit at the presidential mansion, before rushing to a round of deliberations with other party leaders that will last till Friday.

The deliberations will begin with the Democratic Left chief Fotis Kouvelis and exclude the neo-fascists of Chryssi Avgi (Golden Dawn) that entered the parliament.

It is the first time since 1989 that a left party leader in Greece gets such a mandate. The left has never ruled in the country's modern history.

Political analysts in Athens gave 38-year-old Tsipras slim possibilities to make it though.

With some 17 percent of votes and 52 seats in the assembly, Tsipras' party needs the backing of at least one of the pro-bailout parties that have dominated the country's politics for over three decades and suffered heavy losses due to their two-year support to the painful austerity program to avert a Greek chaotic bankruptcy.

According to Greek media commentators, Evangelos Venizelos, chief of socialist PASOK party that ranked third, could do so, if SYRIZA would ease his strong rhetoric.

The indications so far are against, they noted, since upon receiving the mandate Tsipras called for a moratorium on debt repayment, an international commission to investigate whether the debt is legal, the rejection of terms of the bailout-deals and the state control of banks.

He also called on Samaras and Venizelos, who negotiated the second bailout package as finance minister, to take back their written support for the deals.

Both pro-bailout party leaders have called for a review of certain terms, but object to radical approaches, warning that Greece can not risk not meeting its commitments, finding itself with no further international aid, getting thrown out of the eurozone and facing a disorderly default.

If Tsipras fails to form a coalition this week, Venizelos gets a last mandate and then Papoulias will summon all party leaders in a final attempt for a unity government before calling new elections on May 17.

The prospect has fuelled fears for the danger of financial turmoil over missed bailout timetables and targets.