ATHENS (AFP) - Greece's charismatic radical left leader Alexis Tsipras on Sunday appeared on track for a second mandate as premier of the crisis-hit nation after a tense election race against his mainstream conservative rivals.

With more than a quarter of the votes counted, the leftwing Syriza party had a larger-than-expected lead of 35 per cent against 28 per cent for the conservatives.

This led the leader of the conservative New Democracy party, Mr Vangelis Meimarakis, to admit defeat.

"It appears that Mr Tsipras' Syriza is first. I congratulate him," he said.

At Syriza party headquarters, the boyish Mr Tsipras was greeted with a huge round of applause by supporters who clapped and shouted when the results of the exit polls were announced, breaking into Italy's revolutionary anthem, Bandiera Rossa, Italian for "Red Flag".

Mr Tsipras earlier Sunday declared he was confident of winning a second mandate to reform and revive the nation's economy after a first tumultuous seven months in power.

Wearing his trademark open shirt and cheery smile, he said after casting his ballot that voters will elect "a fighting government" ready for the "confrontations necessary to move forward with reforms".

Hands-down winner of a January general election, then with 36.34 per cent of the vote, Mr Tsipras resigned in August and called snap elections, gambling crisis-weary Greeks would give him a new mandate despite his controversial austerity deal with European leaders.

After winning office on an anti-austerity ticket, he agreed in July to more punishing austerity for the nation in exchange for its third financial rescue in five years.

He later argued he had effectively saved Greece from a chaotic exit from the eurozone.

But the move alienated many Syriza supporters and split the party, with a fifth of its anti-euro hardline MPs walking out, forcing Tsipras to call the election.

He went to the polls facing a strong challenge from the conservative New Democracy party led by ex-defence minister Mr Meimarakis, who slammed the former leftwing premier for his U-turn with the country's creditors and for his seven chaotic months in power.

Casting his vote, 61-year-old Mr Meimarakis said: "Voters want to send away ... the lies, the misery, the posers and bring truth and real people."

Over 9.8 million Greeks were registered to vote for a new government which, whoever wins, will face the tough task in the next weeks of pushing through painful new tax rises and pension reforms agreed under the three-year bailout deal adopted by parliament last month.

The reforms were agreed in return for a new 86-billion-euro (S$136 billion) international rescue, Greece's third in five years.

Signed days after Greeks overwhelmingly voted "No" to more austerity in a national referendum, the cash-for-reform deal proved controversial, and Sunday many voters went to the polls with a heavy heart.

"Greeks wanted to try out Syriza but saw the results, they're a bunch of liars," 58-year-old conservative voter Marika Geraki said.

"I believe we should suffer for a while, three to five years, and set ourselves free for the sake of our children," said Mr Haris, a 46-year-old unemployed man.

Mr Tsipras became Greece's youngest prime minister in 150 years on taking office and a beacon for anti-austerity campaigners across the European Union.

And even after the U-turn and the broken promises, many voters believe Tspiras has their interests at heart and represents a break with past leaders perceived as corrupt.

"Tsipras, Tsipras, Tsipras, we want new people," 63-year-old Efthymia Xanthou said.

"We want to be done with thieves, first the Germans and then the conservatives and socialists," she said, referring to the two parties that until Tsipras' victory in January had alternated in power for the past 40 years.

Mr Tsipras is hoping for a strong enough majority to implement the reforms.

But in a slap in the face this week, his flamboyant former finance minister Yanis Varoufakis said he would vote for the breakaway hardliners rather than his former boss.

Manolis Alexakis, a political sociologist at the University of Crete, says Greeks are weary after successive votes and never-ending austerity.

"People seem tired," he said. "The message is, please finish whatever should be done."

Mr Meimarakis has cautioned voters against giving a second chance to a politician who publicly admitted he opposed the bailout he himself signed.

"Do you know of any other prime minister who brokered a deal, brought it to parliament, voted for it and signed it, whilst saying he does not believe in it?" Mr Meimarakis told the To Vima weekly.

With nine parties hoping to enter parliament, no group is likely to secure an outright majority and Mr Tsipras's Syriza party could well need an ally from among those he despises.

A close race was also underway for third place between the socialist Pasok party and neo-Nazi Golden Dawn, whose appeal has not dimmed despite its leadership being on trial over the murder of an anti-fascist rapper two years ago.

But exit polls showed Golden Dawn in clear control of third place with 7.35 per cent.