The antiausterity Syriza party appeared to be heading for a clear victory in Greece's January 25 general elections.
An updated projection from an exit poll on state-run TV showed Syriza as having won with between 36 and 38 percent compared to the incumbent conservative New Democracy party of Prime Minister Antonis Samaras with 26-28 percent.
The far-right Golden Dawn and centrist River parties are in a neck-and-neck race for third place.
"This appears to be a historic victory, a message that does not only concern the Greek people," Syriza party spokesman Panos Skourletis said.
"It resounds all over Europe and brings relief," he added.
Samaras's party conceded defeat, with Health Minister Makis Voridis saying, "We lost."
However, it is still unclear whether Syriza has the required 151 parliamentary seats to have an absolute majority and govern the country alone.
The preliminary results are due by 9:30 a.m. local time and the results are being updated through the night.
The possibility of Alexis Tsipras's radical left-wing Syriza party winning the election has raised concerns that Greece could fail to keep up its debt repayments and leave the eurozone.
Tsipras, who wants to renegotiate Greece's 318-billion-euro ($357 billion) debt, has pledged to put an end to highly unpopular austerity measures linked to an international bailout deal.
"The message is that our common future in Europe is not the future of austerity -- it is the future of democracy, solidarity, and cooperation," he told journalists as he voted in Athens.
After voting in the western Pelopponese region, Samaras appealed to undecided voters to ensure Greece stays on the path of stability and reforms.
"Today we decide if we go forward with strength, security, and confidence, or if we enter into adventures," he said.
Unemployment is around 25 percent and the economy has shrunk by a quarter since the start of the eurozone crisis.
Greece's economy emerged from recession last year for the first time in six years.
German Chancellor Angela Merkel, who is seen as being behind the EU's austerity push, said on January 23, "I want Greece, despite the difficulties, to remain part of our story."