Greece's two main parties, which back tough austerity measures, have lost their parliamentary majority, throwing the country into political uncertainty.
Between them, Pasok and New Democracy attracted less than a third of the vote in elections on Sunday.
A radical left coalition (Syriza) came second after New Democracy, and a neo-Nazi party polled almost 7%.
Greece has secured two EU-IMF bailouts but the result is seen as a rejection of their stringent demands.
With about 99% of votes counted, centre-right New Democracy (ND) is leading with 18.9%, down from 33.5% in 2009.
ND and the socialist Pasok have between them run Greece since the 1970s. Since November, they have been in a coalition led by technocrat Prime Minister Lucas Papademos.
Pasok could only manage third place with 13.2%, down from 43.9% in the last elections and behind Syriza, which polled 16.7% and opposes the government's austerity measures.
The neo-Nazi Golden Dawn party, with almost 7% of the vote, is on course for at least 20 seats in parliament.
There is widespread anger across Greece to harsh measures imposed by the government in return for international bailouts.
New Democracy leader Antonis Samaras said he would form a national salvation government to keep the country in the euro.
But he said he would seek to "amend" Greece's controversial EU-IMF bailout agreement in order to boost growth.
Syriza leader Alexis Tsipras said he wanted to form a left-wing coalition rejecting the terms of Greece's bailouts.
"The parties that signed the memorandum (with the EU and the IMF) are now a minority. The public verdict has de-legitimised them," he said.
"Our proposal is a left-wing government that, with the backing of the people will negate the memorandum and put a stop to our nation's predetermined course towards misery."
Pasok leader and former Greek Finance Minister Evangelos Venizelos called for a broad coalition government of pro-European parties.
"A coalition government of the old two-party system would not have sufficient legitimacy or sufficient domestic and international credibility if it would gather a slim majority," he said.
"A government of national unity with the participation of all the parties that favour a European course, regardless of their positions toward the loan agreements, would have meaning."
He added: "For us in Pasok, today is particularly painful. We knew the price would be heavy and we had undertaken for a long time to bear it."
Pasok was in power when Greece negotiated the terms of its 2010 bailout of 110bn euros (£88bn; $143bn) and was in a coalition with New Democracy when it secured this year's 130bn euro deal.
In fourth place in the partial results were the new right-wing Independent Greeks with 10%.
Their leader, Panos Kammenos, has already ruled out co-operation with either Pasok or New Democracy, Athens News reported.
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 hold another election - a prospect which would alarm the country'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 11bn 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 unprecedented if no party won more than 20% of the vote.
"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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