The June 3 election comes after months of political turmoil and a power vacuum following the botched attempt by former leader Yoon Suk Yeol to impose martial law.
The liberal Democratic Party's candidate Lee Jae-myung, the frontrunner in the polls before a blackout period banning opinion polls began on Wednesday, cast his ballot in Seoul.
"In order to overcome the current crisis... and start again as a Korea of recovery and growth, please vote," Lee said after casting his ballot at a university district in the city.
Lee has pledged to establish a new Ministry of Climate and Energy to "respond to the climate crisis", and expand and reorganise the Ministry of Gender Equality and Family to promote equal rights and deal with any reverse discrimination.
Some 3,107,164 people, or seven per cent of total eligible voters, had voted as of Thursday morning local time, according to National Election Commission data, the highest turnout for the equivalent period in a presidential poll.
South Korea has 44.39 million eligible voters and early voting is allowed on Thursday and Friday.
The top three candidates based on the last published Gallup Korea poll before the blackout period put Lee at 49 per cent public support, followed by his main conservative rival Kim Moon-soo of the People Power Party with 35 per cent and another conservative candidate, the New Reform Party's Lee Jun-seok, on 11 per cent.
Kim and Lee Jun-seok also voted on Thursday.
Kim had eroded what was a more than 20 percentage point gap with Lee Jae-myung at the start of the campaign on May 12, but has failed to convince Lee Jun-seok to drop out and back him to improve his chances.
