Greek leftist Alexis Tsipras made a last call on Sunday for weary voters to return him to power in a close-fought election, after a tumultuous year that saw him cave in to European demands for austerity to keep the country afloat.

Both Tsipras and his conservative rival Vangelis Meimarakis, vying to take on the daunting task of steering the country through a refugee crisis as well as painful economic reforms, called for a high turnout as they cast their ballots in an election polls suggest is too close to call.

It is the third time Greeks are voting this year, after an election that catapulted Tsipras to power and a referendum in which voters backed him to spurn the terms of a European bailout, only for him to agree to it anyway.

With voters now exhausted and the major parties effectively in agreement about the bailout, there were signs that turnout might be comparatively light, which could help the Conservatives against the charismatic Tsipras.

Tsipras was voted into office in January promising to halt austerity measures imposed by Europe, which most Greeks blame for worsening one of the deepest depressions of any industrialized country in modern times.

After banks were shut for weeks and the country pushed to the wall, he effectively reversed himself in August to accept the bailout, splitting his leftist coalition and forcing him to resign and call a new vote.

He argues that his tough negotiations with Europeans softened the blow of austerity and helped secure a promise of debt restructuring that would ease Greece's plight.

His opponents say his erratic leadership and grandstanding only prolonged Greece's agony, deepened the economic crisis and obliterated a nascent recovery.

Smiling broadly as he voted in a schoolroom in a working-class suburb of Athens, Tsipras urged his fellow citizens to usher in a new era and "give a mandate for a strong government with a four-year horizon, which is what the country needs."

Final polls on Friday showed his Syriza party running virtually neck and neck with the conservative New Democracy party of Vangelis Meimarakis.

Voting in an upper-middle class part of the city, Meimarakis said Sunday was a day of celebration for voters to banish "greyness, falsehoods and misery... and bring in authentic people for a better tomorrow for all Greeks."

DISILLUSIONED

Many voters sounded disillusioned with politics.

"What we are hoping for is for the less useless (politician) so he does the least damage to Greece," said 77-year-old Yiannis outside a polling station in Athens.

Apostolos Anastasiou, 73, said he hoped for good cooperation among parties "so that we can see something better happening."

Although the two big parties are close, a slight edge is important since the Greek system gives 50 extra seats in the 300-seat house to the party that places first, as a way to encourage stronger governments.

Nevertheless opinion polls suggest neither Syriza nor New Democracy would secure the 38 percent or so that should offer a majority of seats.

Either would probably seek to set up a coalition with smaller parties rather than a "grand coalition" with the other big force. Tsipras has ruled out cooperating with New Democracy and Meimarakis says he will not join an alliance with Tsipras in a top role.

Golden Dawn, a far right party whose leaders have been charged with setting up a criminal organization, could place third. Such a result would also weigh against the two big parties forming a grand coalition, since that would make Golden Dawn the official opposition, which all mainstream parties say should be avoided.

Voting started at 0400 GMT but around five hours later turnout was still at a pace that appeared lower than in recent elections. One polling station in an Athens suburb recorded only 25 voters in the first three hours, broadcaster ERT said.

Staff at another station in central Athens told a Reuters photographer around midday that turnout had been around 10 percent or less of the electorate so far.

"I hope the abstention rate is low and people go and vote," said Stavros Theodorakis, leader of centrist party To Potami, a potential coalition partner for either of the bigger parties. "We must talk, rule out the possibility of new elections which nobody wants."

Polling is scheduled to end at 1600 GMT, followed immediately by an exit poll and with an early vote projection expected by 1800 GMT. Just under 10 million Greeks are eligible to vote.