Sunday's vote was seen as crucial for Europe and the world, since it could determine whether Greece was forced to leave the joint euro currency, a move that could have potentially catastrophic consequences for other ailing European nations and the global economy. As central banks stood ready to intervene in case of financial turmoil, Greece held its second national election in six weeks after an inconclusive ballot on May 6.
With 37.4 percent of the vote counted, official results showed the conservative New Democracy with 30.5 percent of the vote, ahead of the radical anti-bailout Syriza party's 26 percent and the pro-bailout Socialist PASOK with 12.9 percent.
Although official projections late Sunday showed that no party will win enough seats in the 300-member parliament to form a government on its own, Greece's two traditional parties - New Democracy and PASOK - will have enough seats to form a coalition together.
"The Greek people today voted for Greece to remain on its European path and in the eurozone," New Democracy leader Antonis Samaras said, adding that voters chose "policies that will bring jobs, growth, justice and security. "
His party beat Syriza, which wanted to cancel Greece's international bailouts. Syriza chief Alexis Tsipras has conceded the election.
The parties vying to win have starkly different views about what to do about the ?240 billion ($300 billion) 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.
The party that comes first in Sunday's vote gets a 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.
Virtually unknown outside of Greece four months ago, Tsipras and his party shot to prominence in the May 6 vote, where he came a surprise second and quadrupled his support since the 2009 election.
Tsipras, has vowed to rip up Greece's bailout agreements and repeal the austerity measures, which have included deep spending cuts on everything from health care to education and infrastructure, as well as tax hikes and reductions of salaries and pensions.
But his pledges, which include canceling planned privatizations, nationalizing banks and rolling back cuts to minimum wages and pensions, have horrified European leaders, as well as many Greeks.
"We have beaten fear. Today we open a road to hope," Tspiras said as he voted Sunday. "Today we open a road to a better tomorrow, with our people united, dignified and proud. In a Greece of social justice and prosperity, an equal member of a Europe that is changing."
Samaras, meanwhile, cast Sunday's choice as one between the euro and returning to the drachma. He has vowed to renegotiate some of the bailout's harsher terms but insists the top priority is for the country to remain in Europe's joint currency.
"Today the Greek people speak. Tomorrow a new era for Greece begins," Samaras said after voting in southern Greece.
Earlier 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 Sunday 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.
Menelaos Hadjicostis, Demetris Nellas and AP television in Athens contribute Samaras: "The Greek people today voted for Greece to remain on its European path and in the Eurozone. It voted for those policies that will bring jobs, growth, justice and security