Evangelos Meimarakis and Kyriakos Mitsotakis are to battle it out in a second ballot on January 10 to become New Democracy leader.
The two men were said to be clear leaders in the four-way election carried out on Sunday, although final results were not expected until Monday morning.
Mitsotakis delivered a brief speech on Sunday night indicating he was certain of being in the second ballot and thanking the “silent majority” for backing him.
It is thought that the ex-administrative reform minister trailed the former interim leader Meimarakis but that the latter was several percentage points short of the 50+ percent he needed to win from the first round.
More than an hour after Mitsotakis indicated he would be in the run-off vote a month later, the likely third-placed candidate Apostolos Tzitzicostas conceded that he would not be making the next ballot.
Former health minister Adonis Georgiadis was expected to come last of the four candidates that ran in Sunday’s ballot.
It is estimated that some 400,000 people voted, which was more than the conservatives had expected and forced them to keep polling stations open beyond the original 7 p.m. deadline.