New Democracy’s central electoral committee said its election of a new leader has been delayed because of a computer system malfunction.
The conservative party says that the company hired to provide system support "did not fulfill its contractual obligations" making it "technically impossible" to hold the election Sunday.
Over the past 10 years, Greece's socialist party and the conservatives have been electing their leaders by popular vote rather than through a party congress. New Democracy had hoped to entice hundreds of thousands of voters to take part. Instead, those who began showing up at 7am local (0500 GMT) were unable to cast their votes.
Four candidates, three of them ex-ministers, are vying for the leadership.