Political parties supporting Greece's international bailout will begin forging a government on Monday after an election victory over radical leftists staved off the prospect of the debt-laden country leaving the euro and brought relief to global markets.

Conservative New Democracy leader Antonis Samaras called for broad support after winning Sunday's election over the radical SYRIZA party, which had threatened to cancel the aid deal in defiance of the country's lenders.

"There is no time to waste," Samaras told reporters in Athens as jubilant, chanting supporters waved blue party flags.

"A national salvation government must bring economic growth and reassure Greeks the worst is over," he said.

With 99 per cent of ballots counted, New Democracy had won 29.7 per cent of the vote, ahead of SYRIZA on 27 per cent. Samaras will need the support of the once-mighty PASOK Socialists, now humbled by angry Greeks, to form a government.

A 50-seat bonus given to the party which comes first would give New Democracy and PASOK 162 seats in the 300-seat parliament, in an alliance broadly committed to the 130 billion euros ($164 billion) bailout.

Relegated to third place in an earlier, inconclusive May 6 election, PASOK said it wanted a broad coalition that would include SYRIZA, but most important was to form a government and put an end to the political uncertainty battering Greece and world financial markets.

PASOK officials told Reuters that a party meeting on Monday would decide how the socialists would support Samaras - by participating fully in government, or by voting with the coalition in parliament.

The new government might get a helping hand from its eurozone peers with Germany's foreign minister suggesting Athens might get more time to implement the cuts demanded of it.

But most economists say even that would leave Greece, into a fifth year of deep recession, facing a program it cannot hope to deliver on.

The election result brought cheers and smiles at both the headquarters of New Democracy and SYRIZA.

The leftists rode a huge wave of discontent over austerity and chronic corruption, viewing second place as a victory for a party that has long been on the fringes of Greek politics.

SYRIZA leader Alexis Tsipras, 37, made clear his was now the main opposition party, swearing to fight on against the bailout and take power sooner or later.

"Very soon, the Left will be in power," the former communist and student protest leader told elated supporters in central Athens after conceding defeat. "We begin the fight again tomorrow."

SHORT-LIVED RELIEF

The result came as a relief for Greece's EU and IMF lenders and eurozone partners who feared a SYRIZA victory would tip Greece over the edge and the common currency towards break-up.

But the vote revealed a society deeply split between its desire to stay in the euro and a deep-seated anger at the harsh salary, pension and job cuts that have hit the poorest sections of society, sparing a political and business elite seen as widely seen as corrupt.

"We will now have a strong parliamentary opposition to help overturn the bailout," said Giorgos Argyropoulos, 25, a clerk at an electronics store who voted for SYRIZA.

Analysts say a pro-bailout coalition could yet be short-lived, having commanded not much more than 40 per cent of the vote and pressed by lenders for more austerity measures squeezed from a society that says it cannot give anymore.

More than two years of budget cuts have caused unemployment to jump to over 22 per cent. Businesses are shutting down by the dozen and the homeless are multiplying on the streets of Athens.

Both New Democracy and PASOK have said they want to renegotiate the terms of the bailout with international lenders, to spread the burden on people over a longer period and take measures to boost growth.

Greece's EU partners and the IMF welcomed the pro-bailout parties' victory, saying they were ready to work with the government that would emerge. But EU officials have made clear Greece must stick to its pledges to receive more funding.

However, there may be some leeway at the margins.

"There can't be substantial changes to the agreements but I can imagine that we would talk about the time axes once again, given that in reality there was political standstill in Greece because of the elections, which the normal citizens shouldn't have to suffer from," German Foreign Minister Guido Westerwelle said.

Even so, Greece is in a desperate situation.

Its caretaker government says the state has enough cash to last a few weeks and Athens pledged to come up with an additional 11.7 billion worth of spending cuts in June to merit the next loan installment.

In a surprising turn that underscored the fragmentation of Greek society, the ultra-right Golden Dawn party looked set to win 18 seats, repeating its success of May 6 despite a now-notorious incident in which its spokesman threw water at one leftist opponent and slapped another during a TV debate.

The incident appeared to have boosted their standing, to the shock of pollsters who predicted the opposite.