Greece raced to form a coalition with broad support by the end of Monday after an election victory by pro-bailout parties which eased fears of a Greek eurozone exit and brought relief to world markets.

"There is a categorical imperative to form the government" today, President Carolos Papoulias before giving a formal mandate for negotiations to conservative leader Antonis Samaras whose New Democracy party won the election.

"The country cannot remain ungoverned for even an hour," Papoulias said.

Samaras called for "national understanding" on a new government and said he would begin consultations with the election runners-up at 1100 GMT.

He also said there should be amendments to the conditions of an EU-IMF bailout deal "so the Greek people can escape from today's torturous reality."

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 but which has called for other leftist parties to be included.

Europe and the United States urged Greece to act quickly to form a new government and proceed with urgent reforms in order to meet the terms of bailout loans that have kept the Greek economy on life support for the past two years.

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.

"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.

Political analyst Yiannis Loulis said: "The government will be fragile, with a fragile popular base, and I do not think it is going to last very long.

"It was mainly a vote of fear against the exit from the euro, not a real support of the reforms," he said.

The eurozone is hoping the result can draw a line under a lengthy period of uncertainty that has unsettled markets.

Global stock markets initially rallied after the result and the euro rose against the dollar but those gains later petered out.

In foreign exchange deals on Monday, the euro was up just $1.2648 from $1.2644 late on Friday in New York.

The Greek stock market was up 5.65 percent in afternoon trading.

Sunday's election was the most critical for Greece since the end of military rule in 1974 and was particularly significant for Europe as Greece is where the debt crisis kicked off in 2009 before spreading across the continent.

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

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

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.

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 at 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 also 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. It has also been given a 107 billion euro private debt write-off.