South Korea's ruling Democratic Party that supports President Moon Jae-in is scheduled to select its presidential candidate early next month.
The six contenders include Lee Jae-myung, who is the governor of Gyeonggi Province outside Seoul, and former prime minister and party leader Lee Nak-yon.
The outcome of the vote that will take place by region will decide the candidate for the presidential election scheduled for next March.
Party members cast their ballots at the first polling station set up in the central city of Daejeon on Saturday.
A survey released by Gallup Korea on Friday shows Lee Jae-myung has the highest support at 24 percent as the person most suitable to be the next president.
The figure is 16 percentage points higher than that of Lee Nak-yon.
Fifteen contestants, including former prosecutor general Yoon Seok-youl who resigned due to being at odds with Moon's administration, are running in the presidential race of the main opposition People Power Party.
The party is scheduled to decide on its candidate in November.