The head of the conservative New Democracy party raced Monday to form a coalition after an election win which eased fears of a Greek eurozone exit and caused widespread relief on the markets.

"The country does not have a minute to lose," said Antonis Samaras after New Democracy won 129 of the 300 parliamentary seats in Sunday's vote, opening the path for a coalition with the third placed socialist party Pasok which has 33.

"We ask all political forces which share the aim of keeping the country in the euro... to join a government of national unity," Samaras added.

Both New Democracy and Pasok have vowed to enact the austerity measures set out in bailout deals worth more than 200 billion euros struck with the European Union and International Monetary Fund in a bid to avert Greek bankruptcy.

The anti-austerity leftist Syriza party and its firebrand leader Alexis Tsipras came second with 71 seats. It has ruled out joining a coalition, saying the harsh conditions for the bailout deal should be scrapped altogether.

President Carolos Papoulias is due to meet Samaras at 0930 GMT and task him with forming a government.

Greek news reports said Samaras and Pasok leader Evangelos Venizelos had already broached the topic of a coalition in a phone conversation late Sunday.

The eurozone is hoping the result can draw a line under a lengthy period of uncertainty and European Union leaders were quick to call on Greece to enact key reforms after its second general election in two months.

Greek stocks opened with a 6.48-percent jump and kept on climbing ahead of the meeting between Samaras and Papoulias at which the conservative leader will be given three days to form a cabinet.

Pasok has said it is ready to join a coalition with New Democracy but wants other leftist forces to be included in a government of "national responsibility" with a broad mandate for reforms.

Relieved Asian markets surged on the news with Tokyo closing up 1.77 percent and Hong Kong climbing 1.55 percent. The euro also rose sharply to $1.2720 compared to $1.2644 late on Friday.

The elections were being seen as an important milestone in the austerity or growth debate in Europe, with extra significance in Greece where the sovereign debt crisis started in 2009 setting off a chain reaction across Europe.

"A further lapse into the unknown was avoided" with the New Democracy victory, said Unicredit economist Erik F. Nielsen.

But he warned that the past "six weeks since the last election have seen an already very weak economy grind to a halt" and there is "much to be done".

Japan and Australia joined in EU and US calls for Greece to form a new cabinet quickly.

IMF chief Christine Lagarde added to the sense of urgency ahead of the vote saying consultations should start as early as this week as there was uncertainty about exactly what reforms Greece had implemented.

"We take note of the election results in Greece and stand ready to engage with the new government on the way forward to help Greece achieve its objective of restoring financial stability, economic growth and jobs," the IMF said.

Samaras has called for a moderate renegotiation of the multi-billion bailout, which has kept the Greek economy on life support but has also imposed steep salary and pensions cuts in a country now in its fifth year of recession.

"There is no alternative to a coalition between the right and the socialists since the key issue at stake was the formation of a pro-euro government," Thomas Gerakis, head of the Marc polling institute, told AFP.

Anni Podimanta, a Greek socialist member of the European parliament, said on Net public television: "There needs to be a government as quickly as possibly but not one that will fall in two or three months.

"The parliamentary majority is large but it needs as large a social base as possible," she said, adding: "The government has to be able to negotiate with its partners and they want a Greek interlocutor who is credible and stable."

Key players including Germany said as soon as results began filtering through that they were ready to negotiate postponing Greek budget deadlines -- an apparent quid pro quo after Chancellor Angela Merkel urged a pro-bailout vote.

Merkel was the first European leader to call Samaras, saying she would work together with him "on the basis that Greece will meet its European commitments."

Tsipras accused Samaras during the campaign of defending "Merkel's Europe of the past" while Samaras said Tsipras would bring back the drachma currency.

Any new government in Greece faces daunting economic challenges in a country where unemployment is 22.6 percent and a tricky political balancing act between pressure from the streets and from the global financial community.

Victory celebrations were extremely muted in Athens on Sunday with just around 100 New Democracy supporters showing up at a victory rally with Samaras in central Syntagma square, the scene of multiple anti-government protests.

The sense of disillusionment with the political establishment was reflected in the strong showing by the neo-Nazi Golden Dawn party which won 18 seats after capitalising on anti-immigrant fears.

Although the immediate risk of a eurozone exit has receded with Syriza's defeat, some analysts have warned that the stricken country could eventually still have to leave the euro even with a New Democracy-led government.

Greece has been forced to seek bailouts twice, first for 110 billion euros in 2010 and then for 130 billion euros this year plus a 107 billion euro private debt write-off -- for a total of 347 billion euros ($439 billion).