The latest polls put centre-right New Democracy in the lead with 19-20.5% of the vote, down from 33.5% in 2009.
Centre-left Pasok is put in third place with 13-14%, down from 43.9%. Syriza, a left-wing coalition, is put ahead of it in second place with 15.5-17%.
Pasok and New Democracy, in coalition since last November, were expected to lose support to anti-austerity parties.
There is widespread anger across Greece to harsh measures imposed by the government in return for international bailouts.
Syriza opposes the government’s austerity measures.
The neo-Nazi Golden Dawn party could enter parliament for the first time if the exit poll prediction of it winning 6.5 -7.5% of the vote comes to fruition.
The first official results are expected later on Sunday night.
“The truth is here – the reality of this result is that at the moment this produces no government,” said Theodoros Pangalos, outgoing deputy prime minister and senior Pasok official.
“It is not a question at the moment of who gets a little more or a little less.”
If no party wins enough votes to form a government, the winner will have to seek a coalition with rivals.
Coalition negotiations can take place over three days. If they fail, the party in second place can try to form a coalition, and if still unsuccessful, the third party will receive the mandate.
If still no coalition emerges, Greece will go to another election – a prospect which would alarm Greece’s international creditors.
The ability of any new government to carry on with the austerity programme will be crucial for Greece’s continued access to bailout funds from the EU, the European Central Bank and the International Monetary Fund – the so-called Troika.
Any political instability may prompt fresh questions over the country’s place in the eurozone.
Under the current plan, a further 11 billion Euros of savings in spending are due to be found in June.
Othan Anastasakis, director of south-east European studies at Oxford University, said it would be “incredible” if no party won more than 20% of the vote.
“This is really unprecedented,” he said.
“The whole landscape becomes even more unpredictable after the election. We don’t know if there will be a coalition or how long it will survive. I don’t see it surviving very long.
“Greeks are sending a very strong message abroad, which is <<enough with austerity>>.”
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