The European Union and the United States said Greece now had to enact key reforms after its second general election in two months handed victory to the conservative New Democracy party, which has pledged to keep Greece in the euro.
New Democracy leader Antonis Samaras, a Harvard-educated former foreign minister, said after Sunday's win: "The country does not have a minute to lose."
"We ask all political forces which share the aim of keeping the country in the euro... to join a government of national unity," he said.
The third-placed socialist Pasok party 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 per cent and Hong Kong climbing 1.55 per cent. The euro also rose sharply to $1.2720 compared to $1.2644 late on Friday.
The anti-austerity leftist Syriza party and its firebrand leader Alexis Tsipras came second and has ruled out joining a coalition, arguing that the harsh conditions for the bailout deal should be scrapped altogether.
With almost all the votes counted, New Democracy controlled 129 seats in the 300-seat parliament, Syriza 71 and Pasok 33. The neo-Nazi Golden Dawn party which capitalised on anti-immigrant fears also won 18 seats.
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.
International Monetary Fund 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, a political analyst and head of the Marc polling institute, told AFP.
Anni Podimanta, a Greek socialist member of the European parliament, said in a political talk show 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."
A deadlock like the one seen last month and another election are seen as highly unlikely outcomes of the coalition talks in which New Democracy will be given a maximum of three days by the president to form a government.
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 per cent and a tricky political balancing act between pressure from the streets and from the global financial community.
Victory celebrations were extremely muted here 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.
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).