Greek lawmakers failed to elect a new president in the first round of voting on Saturday.
One of the candidates pushed by political parties needed a majority of 200 votes in the 300-seat parliament to take the largely ceremonial post.
A second round is scheduled for 31 January, but is also expected to be inconclusive.
After two rounds, the required majority falls to 180 votes and then to 151. The final vote requires a simple majority of those present.