Thousands of supporters of Greece's left-wing Syriza party celebrate in the streets of Athens as the party leader Alexis Tsipras claims victory over austerity.

Thousands of Greeks have taken to the streets to celebrate the victory of the leftist Syriza party, dancing and singing in a plaza in central Athens known as the Square of Tears for its tragic past.

"Greeks have shed tears of sorrow in this very square, and now they are finally shedding tears of happiness and hope for a new tomorrow for the country," 44-year-old taxi driver Giorgos Balabanis said late on Sunday.

In modern Greek history, the square has been connected with the 1942 rounding up of Greece's Jewish population by occupying German forces.

Getty Images VICTORY: Supporters of Alexis Tsipras, leader of Syriza left-wing party, cheer during a victory rally outside Athens University Headquarters on Sunday.

More recently it has been the scene of violent anti-austerity demonstrations and riots over the last five years, which resulted in the deaths of three employees in a torched bank nearby.

Late Sunday, folk and revolutionary songs blasted from loud speakers to a crowd of happy revellers.

"People are finally celebrating and feeling happy for the hope that is coming and the responsibility for what we need to do," 50-year-old school teacher Sofia Korsavidou said.

"We have had enough of endless austerity, the unemployment, the suicides and the misery, which has been brought upon the Greek people.

"This is a new era not only for Greece but for all of Europe — the people, not the banks, have the power."

'HUMILATION AND SUFFERING'

After his Syriza party swept to victory in a snap election on Sunday (local time), Greek leftist leader Alexis Tsipras promised that five years of austerity, "humiliation and suffering" imposed by international creditors were over.

With over 99 per cent of the vote counted, Syriza had 149 seats in the 300-seat Parliament, taking 36.3 per cent of the vote, 8.5 points ahead of the conservative New Democracy party of Prime Minister Antonis Samaras.

Tsipras is expected to hold coalition talks on Monday with the small Independent Greeks party which, like Syriza, opposes Greece's bailout deal with the European Union and International Monetary Fund.

While Tsipras fell just short of an overall majority, he is set to lead the first euro zone government committed to overturning the kind of budgetary rigour that was imposed on Greece as a condition of the bailout in 2010.

"Greece leaves behind catastrophic austerity, it leaves behind fear and authoritarianism, it leaves behind five years of humiliation and suffering," Tsipras told thousands of cheering supporters gathered in Athens.

Syriza's victory marks a flat rejection of the model for troubled euro zone economies championed by German Chancellor Angela Merkel. It is also likely to strengthen calls for the euro zone to move towards policies which promote economic growth, rather that tackling budget deficits.

Syriza's campaign slogan "Hope is coming!" resonated with voters worn down by huge budget cuts and heavy tax rises during the years of crisis that have sent unemployment over 25 per cent and pushed millions into poverty.

"We hope our expectations will be fulfilled," said 47-year-old teacher Efi Avgoustakou. "On Monday in class, we're not allowed to comment and take sides but we will be smiling."

Financial markets reacted nervously to the victory of Tspiras, who has promised to renegotiate Greece's debt agreements, fearing potential conflict with other euro zone governments that could put more strain on the currency bloc.

The euro slid to near an 11-year low and U.S. stock futures fell as Asian markets opened on Monday.

Germany has insisted Greece must respect the terms of its 240 billion euro bailout deal, which saved the country from bankruptcy but at the cost of bitter sacrifices by the Greek people.

'LOST DIGNITY'

Tsipras said he would cooperate with fellow euro zone leaders for "a fair and mutually beneficial solution" but said the Greek people came first. "Our foremost priority is that our country and our people regain their lost dignity," he said.

He has promised to keep Greece in the euro and toned down some of his rhetoric, but his arrival in power is likely to encourage other anti-austerity parties which are winning support across Europe, such as the Podemos movement in Spain.

It might also strengthen the hand of mainstream leaders including French President Francois Hollande and Italian Prime Minister Matteo Renzi who argue that orthodox austerity policies have failed to produce the economic growth which Europe needs to recover fully from the global financial crisis.

Hollande expressed in a statement his "desire to pursue the close cooperation between our two countries in service of growth and the stability of the euro zone".

Finnish Foreign Minister Erkki Tuomioja was more forthright, saying he believed the result would change the debate in Europe and put more emphasis on growth and employment. "This is a slap at what I see as a very right-wing economic policy in Europe," Tuomioja, a Social Democrat, told the website of the Helsingin Sanomat newspaper.

However, with Greece's economy unlikely to see any quick recovery from its crisis, Tsipras faces enormous problems and his victory raises the prospect of tough negotiations with European partners including Merkel.

Greece's bailout deal with the euro zone is due to end on February 28 and Tsipras' immediate challenge will be to settle doubts over the next installment of more than 7 billion euros in international aid. EU finance ministers are due to discuss the issue in Brussels on Monday.

One Syriza official expressed confidence that Tsipras could form a government by Wednesday.

Political analyst John Loulis doubted a minority government would be viable. "It's a historic win," he said, adding that Tsipras would have to form a coalition to prevent renewed instability. "He has no other option, the last thing the country needs would be another round of elections."

STANDOFF WITH BERLIN

Tsipras has promised to renegotiate agreements with the European Commission, European Central Bank and International Monetary Fund "troika" and write off much of Greece's 320 billion-euro debt, which at more than 175 per cent of gross domestic product, is the world's second highest after Japan.

Coming after the ECB's move to pump billions into the bloc's flagging economy, Sunday's result will stir consternation in Berlin. A senior lawmaker in Merkel's conservative party said the result showed Greek voters had turned away from austerity but he said Europe could not accept rejection of the bailout.

"We must not reward the breaching of agreements," Wolfgang Bosbach told the daily Osnabruecker Zeitung newspaper. "That would send completely the wrong signal to other crisis-stricken countries that would then expect the same treatment."

Tsipras wants to roll back many of the measures demanded by the "troika", raising the minimum wage, lowering power prices for poor families, cutting property taxes and reversing pension and public sector pay cuts.

US investment bank J.P. Morgan said the result could weigh on markets but that it considered speculation over a possible Greek exit from the euro was "a stretch" and a negotiated deal appeared the most likely outcome. "Our base case remains that a Syriza government or Syriza-dominated coalition would alter its platform to retain troika financing," it said.

Greece, unable to tap the markets because of sky-high borrowing costs, has enough cash to meet its immediate funding needs for the next couple of months but it faces around 10 billion euros of debt repayments over the summer.