Greece's socialist prime minister and conservative opposition leader have met at the office of the Greek president to try to agree on a power-sharing coalition that would secure continued bailout funds for the country and avert a national bankruptcy.

Officials said the talks between Prime Minister George Papandreou and New Democracy party chief Antonis Samaras began Sunday evening local time.

Earlier, the prime minister told an emergency cabinet meeting that he wants to reach a deal by the end of the day on a national unity government that would be led by someone else. Such a government would be tasked with securing parliamentary approval of a second European-led bailout package offered to Greece last month. The deal requires Greece to increase tax rates and make deeper cuts in government pensions and salaries.

Samaras met with ceremonial President Karolos Papoulias earlier Sunday and reiterated a demand for Mr. Papandreou to resign before any political negotiations. But, members of the ruling Pasok party said the prime minister will resign only after the government and the opposition reach a deal on a coalition, including how long it will lead the country until new elections.

The ruling socialists say elections should wait until February, but the conservative opposition wants a vote by December.

Ruling party members also said they do not want to leave Greece without a government on Monday, when the Greek finance minister is supposed to meet with his counterparts from the euro zone in Brussels.

European leaders have called on Greece to approve the new bailout plan and implement the terms of an existing rescue package provided to Athens by the European Union and International Monetary Fund last year. Some EU leaders have warned that Greece will not get any further aid if it fails to take those measures.

Greek Finance Minister Evangelos Venizelos has said Greece needs the next $11 billion installment of its existing bailout by December to avoid bankruptcy.