The pro-bailout New Democracy party came in first in Greece's national election, and its leader has proposed forming a pro-euro coalition government.
New Democracy leader Antonis Samaras says "the Greek people today voted for Greece to remain on its European path and in the eurozone.''
He says voters chose "policies that will bring jobs, growth, justice and security.
His party beat the anti-bailout Syriza party, which wanted to cancel Greece's international bailouts.
Syriza chief Alexis Tsipras has conceded the election.
It was Greece's second national election in just six weeks to try to select a new government after an inconclusive ballot on May 6.
The overnight vote (NZ time) was seen as crucial for Europe and the world, since it could determine whether Greece is forced to leave the joint euro currency, a move that could have potentially catastrophic consequences for other ailing European nations and the global economy.
The conservative New Democracy and the socialist PASOK are seen as traditional parties within Greece, and their coalition will need at least 151 seats to form a majority government.
The parties vying to win the weekend election had starkly different views about what to do about the 240 billion euro in bailout loans that Greece has been given by international lenders.
Greece has been dependent on rescue loans since May 2010, after sky-high borrowing rates left it locked out of the international markets following years of profligate spending and falsifying financial data. The spending cuts made in return have left the country mired in a fifth year of recession, with unemployment spiraling to above 22 percent and tens of thousands of businesses shutting down.
New Democracy leader Antonis Samaras said his top priority is to stay in the euro but has promised to renegotiate some terms of the bailout.
Syriza had vowed to cancel the terms of Greece's international bailout deal and repeal its austerity measures.
"There are many power-sharing possibilities that include a vote of tolerance from parties,'' Syriza member Nikos Voutsis said on state television. "But we'll see.'''
The party that came first in the vote gets an automatic bonus of 50 seats in the 300-member Parliament and gets the first try at forming a new government with a majority in Parliament. If they fail, the next highest party gets to try.
There are no rules governing a country's exit from the eurozone. A Greek exit could cause economic chaos in Europe, prompt investors to flee stocks in the U.S. , and spark a panic that other debt-strapped European nations Portugal, Ireland, Spain and Italy might also have to leave the eurozone.
That domino scenario known in economic terms as contagion could engulf the euro, causing a global financial panic not unlike the one that gripped the world in 2008 after the investment firm Lehman Brothers failed in the U.S.
Earlier on Sunday, about 10 men armed with sledgehammers and wooden bats attacked a polling station in central Athens, wounding two policemen guarding it and setting fire to the ballot box shortly before polls closed. The attack the only one reported so far took place in the Athens neighborhood of Exarhia, a traditional haven for leftists and anarchists.
Greek police were also investigating the discovery of two unexploded hand grenades outside private Skai television station on the outskirts of Athens. Greek government spokesman Demetris Tsiodras denounced the devices as an attempt to spoil the smooth running of the election.