ATHENS Greece's leftists will receive an official mandate on Tuesday to form a coalition government after an inconclusive national election, but are expected to seek a second vote instead.

The conservative New Democracy party romped to victory with 40.8% of the vote in Sunday's poll which sent the leftist Syriza into a tailspin after taking 20.1% of the vote.

Greek Prime Minister Kyriakos Mitsotakis, a member of New Democracy, declined to seek a coalition on Monday, paving the way for a second vote on June 25 that he hopes his conservative party will win outright.

Without New Democracy, opposition parties do not have enough seats to form a ruling alliance, and all party leaders have indicated they will not hold exploratory talks. Syriza said that "the final battle" had yet to come.

"In the coming election our primary responsibility is to prevent the prospects of an almighty and uncontrollable ruler-prime minister," Syriza leader Alexis Tsipras said in a televised statement on Monday. "But also to protect the leading presence of the left in this country's political landscape."

The country's president, Katerina Sakellaropoulou, was due to meet Tsipras at 0800 GMT and hand him a mandate to try to form a coalition government.

Syriza's defeat revealed a split left. Two small leftist parties, set up by former Syriza members, did not make it into parliament.

During the pre-election period, Syriza tried to persuade the Socialist PASOK party, which finished third in Sunday's election, and leftist parties, including the Communist KKE, to back it in a coalition government.

But after its defeat, Syriza accused them of turning their back on its efforts to form a broader alliance against the conservatives.

If Tsipras returns the mandate to form a coalition, as he has suggested he will, PASOK will get a chance to do so before the president appoints a caretaker government that will lead Greece to a second vote.

That election will take place under a system of semi-proportional representation, with a sliding scale seat bonus, increasing the chances of an outright win for Mitsotakis's party. All parties are eligible to run again.

(Reporting by Renee Maltezou. Editing by Gerry Doyle)