The Greek president is holding talks between socialist Prime Minister George Papandreou and the opposition leader Antonis Samaras.
Papandreou and his Pasok party are under immense pressure to put together a government of national unity to try and find a solution to the country's sovereign debt crisis.
On Friday, Papandreou survived a vote of no-confidence, seemingly opening the way for the eurozone bailout package to pass through parliament.
However, on Saturday Samaras, leader of the opposition New Democracy party, said that they would not take part in a coalition and called for an immediate election.
Papandreou held talks with his cabinet and Pasok MPs, amid reports that he was prepared to resign if a new government could be formed.
This could open the way for a candidate from one of the centre left or centre right parties to take temporary leadership of the country to pass the bailout, with elections reportedly scheduled for December.
Alternatively, Evangelos Venizelos, the current finance minister, could be installed as prime minister. Ether way, Papandreou's time at the top table of Greek politics looks certain to be over, as European leaders push for a quick solution to the political manoeuvrings in Athens.
Speaking on Sky News, Greece's shadow Finance Minister Notis Mitarachi said:
"We want elections but realise the need for an interim government to pass the loan agreement."
"The prime minister should resign opening the way for a new leader."
"We will support interim government but do not want to be part of it."