Ahead of Sunday’s snap vote, both front-runners are vowing to stay in the eurozone – and that means continued austerity.
Greeks have voted in a general election that Alexis Tsipras, the former prime minister, hopes will give him a second chance to lead the country.
Opinion polls in Greece indicate millions of the country’s voters were undecided before Sunday’s polls.
The last voter surveys forecast victory for Tsipras’ left-wing Syriza party over Vangelis Meimarakis, head of the conservative New Democracy party, by margins ranging from 0.7 to three percentage points, the AFP news agency reported.
Both Tsipras and Meimarakis wrapped up campaigning on Saturday.
Tsipras resigned last month forcing early elections.
He won January’s poll on an anti-austerity ticket, but had to accept economic reforms in exchange for a $96bn bailout package from Greece’s international creditors.
With nine parties hoping to enter parliament, whoever wins is unlikely to secure an outright majority and may need to form a coalition.
Tsipras agreed to the eurozone bailout after 61 percent of Greek voters in a July referendum overwhelmingly voted against an earlier offer that insisted on austerity measures.
The bailout Tsipras agreed to, which kept Greece in the eurozone, was widely seen as more severe than the original offer and included new taxes and spending cuts.
While Tsipras’ supporters say he went down fighting, Meimarakis has described his seven months in government as “an experiment that cost the country dearly”.
In January Syriza won the general election with 36.34 percent of the vote, followed by the New Democracy bloc at 27.81 percent.
The ballot boxes for Greece’s 10 million voters opened at 7am local time (4GMT).
With reporting from Barnaby Phillips in Athens