The premier made no statements after the one-hour audience with the President but headed directly to the government headquarters at the Maximos Mansion, and would make an address to the nation later in the day.
Papandreou was also holding a series of telephone contacts with the political party leaders on Wednesday.
He spoke with Communist Party of Greece (KKE) leader Aleka Papariga and Democratic Left leader Fotis Kouvelis before the meeting with the President.
The premier will call main opposition New Democracy (ND) leader Antonis Samaras, Popular Orthodox Rally (LAOS) leader George Karatzaferis, Coalition of the Radical Left (SYRIZA parliamentary alliance) parliamentary group leader Alexis Tsipras and Democratic Alliance leader Dora Bakoyannis after the with the President, and before his address to the people.
Government sources said that the premier was not expected to announce snap elections, an option they said has been ruled out and was not among the topics discussed by Papandreou with the President.
Greece is at a "historically critical" moment, prime minister George Papandreou said on Wednesday, and reiterated his call for national understanding, as he was greeted at the Presidential Mansion by President of the Republic Karolos Papoulias for an extraordinary meeting asked by the premier.
Papandreou said that, even today, he was in contact with the leaders of the other political parties to seek understanding, adding: "Everyone undertakes his responsibilities. I am aware of my responsibilities and the responsibilities of my government towards the Greek people and the country."
"In every instance, we will move ahead, with this sense of responsibility, for the necessary decisions in order for the country to exit the crisis," Papandreou added.
Papoulias stressed the need for a nationwide effort.