Greek conservative Antonis Samaras has three days to form a coalition, faced with EU warnings to keep to the tough terms of international bailouts.
Two-thirds of Greek voters backed parties opposed to the EU/IMF deal, renewing fears that Athens may default on its debts and leave the eurozone.
Germany's Angela Merkel has made clear that Greece's reforms must go on.
But her focus on austerity has taken a knock with the election in France of pro-growth Socialist Francois Hollande.
Mr Hollande campaigned on a platform of renegotiating the terms of the EU fiscal pact to concentrate more on reviving economic prosperity than simply reducing budget deficits.
Mrs Merkel said she would meet France's next president next week "with open arms" but told a news conference that "we in Germany are of the opinion, and so am I personally, that the fiscal pact is not negotiable".
The German chancellor added that the Greek debt reforms were of "utmost importance". That message was underlined by European Commission spokeswoman Pia Ahrenkilde Hansen, who said Brussels "hopes and expects that the future government of Greece will respect the engagement that Greece has entered into".
Any political instability in Greece may prompt fresh questions over the country's place in the eurozone. Under Greece's current bailout plan, a further 11bn euros of cuts in spending is due to be found next month.
News of the Greek vote and the election of Francois Hollande sent the euro falling to its lowest level against the dollar since January. Shares on the Athens stock market tumbled, with the Athex index sliding more than 7% in morning trading.
Although a protest vote against the stringent austerity measures enforced on Greeks had been widely expected, in the event the two main parties that had agreed the bailout terms, New Democracy (ND) and socialist Pasok, attracted less than a third of the vote.
For Greece, it amounts to a political revolution as the country has been run by either one party or the other since the 1970s. Since November, they have been in a coalition, led by technocrat Prime Minister Lucas Papademos, which secured this year's 130bn euro deal.
Pasok was also in power when Greece negotiated the terms of its 2010 bailout of 110bn euros (£88bn; $143bn).
New Democracy's support on Sunday slipped from 33.5% to less than 19% of the vote while Pasok's share plummeted from 43% to just over 13%.
A radical left coalition, Syriza, came second, in front of Pasok, with 16.8% and a party of ultra-nationalists - Golden Dawn - polled almost 7%.
Having polled the most votes, ND leader Antonis Samaras has begun talks to try to convince other parties to join a new coalition, but only Pasok are so far thought likely to show interest. Pasok's leader and former Finance Minister Evangelos Venizelos has 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.
Allowed only three days to seek a deal by President Karolos Papoulias, the centre-right leader has pledged to keep the country in the euro, although he has promised to try to amend the bailout terms in order to boost growth.
His first meeting with Syriza leader Alexis Tsipras, the runner-up in the election, came to nothing.
Mr Tsipras, speaking on Greek TV, said the bailout deal was a "tragedy", and he held out the possibility of a coalition involving "the forces of the left". He has already described the parties that signed the EU/IMF bailout as "de-legitimised" by the public.
Mr Samaras went on to have talks with Pasok's Evangelos Venizelos. He is also due to talk to Fotis Kouvelis from Democratic Left, who has already made clear his objection to a coalition agreement with Mr Samaras.
In fourth place 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.
The extremist Golden Dawn party is on course for at least 20 seats in parliament.
"It is time for those that betray [Greece] to be afraid," its leader Nikolaos Mihaloliakos warned. "We are coming. We are Greeks, nationalists, and we will allow no one to doubt this."
Deal in doubt
If Mr Samaras fails to reach a coalition deal, the party in second place, Syriza, 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.