A presidency statement said they will meet again on Monday to discuss who would head the coalition government, but that > from page 1. Papandreou would not lead the new administration.
"Tomorrow there will be new communication between the prime minister and the opposition leader on who will be the leader of the new government," the statement said.
The statement made no mention of how long the interim government would last.
The European Union gave Greece 24 hours on Sunday to explain how it will form a unity government to enact a bailout agreement.
Earlier, the European Union turned up the heat on bickering Greek politicians on Sunday, pushing them to agree a crisis coalition and demanding progress towards backing an international bailout deal in the next 24 hours.
In a sign that Greece's political deadlock may be easing under EU pressure, a senior socialist said Prime Minister George Papandreou had made clear he would resign once a coalition deal was done, possibly as soon as Sunday night.
Papandreou asked the Greek president to host a three-way meeting with himself and the leader of the opposition on Sunday night after a cabinet meeting to explore the possibility of an agreement soon, the prime minister's office said shortly before the cabinet session ended.
President Karolos Papoulias said he would invite the leaders provided they agreed on a "procedure" beforehand, State TV said.
With euro zone finance ministers due to meet on Monday, senior socialist lawmaker Telemachos Hitiris said: "Everything must be done within the day, otherwise tomorrow it will be hell."
Any new coalition will have three immediate tasks: pushing the euro zone bailout through parliament, completing a bond swap which will halve the value of private creditors' Greek state debt holdings, and passing the 2012 budget.
But it is likely to govern for only a few months, too short a time to finish carrying out reforms demanded by the EU and IMF to make the Greek economy more efficient and competitive.
Earlier, the conservative opposition offered to cooperate in forming a national unity government provided Papandreou stood aside after two years at the helm.
European Economic and Monetary Affairs Commissioner Olli Rehn demanded a Greek unity government to restore confidence, which has been shaken by doubts that Athens would commit itself to the 130 billion euro bailout package. Rehn wanted progress by the time euro zone finance ministers - including Greek Deputy Prime Minister Evangelos Venizelos - meet on Monday night.
"We have called for a national unity government and remain persuaded that it is the convincing way of restoring confidence and meeting the commitments," he told Reuters. "We need a convincing report on this by Finance Minister Venizelos tomorrow in the Eurogroup."
Greece breached confidence with its euro zone partners last week and put itself on a path towards leaving the common currency, Rehn said in a telephone interview.
Papandreou provoked uproar on Monday by announcing a referendum on the bailout, which demands yet more austerity to be imposed on the long-suffering Greek population, plunging his country into political as well as economic crisis.