"It would be advisable that the next South Korean leader respond positively to China's proposal to resume dialogues - Pyongyang suspends its nuclear programme in exchange for the US-South Korean halt of military exercises - something the previous South Korean leaders have failed to do in the past 10 years", a commentary in China's official Xinhua news agency said on Tuesday.
Voting in the country's presidential election began at 6 a.m.at 13,964 polling stations throughout the country, the National Election Commission said.
Voter turnout stood at 5.6 percent by 8am (2300 GMT Monday), according to the National Election Commission.
Early voting took place last Thursday and Friday for the first time in a presidential election since it was introduced in local elections in 2014, with a record-high number of voters participating.
South Korean President Park Geun-hye speaks during an address to the nation last November at the presidential Blue House in Seoul.
Front-runner Moon Jae-in, 64, of the Democratic Party cast his ballot at a polling station in northwestern Seoul, together with his wife.
About 42.4 million South Koreans are eligible to cast their ballots.
Kim Sun-Chul, 59, said he voted for Moon because "this country needs to restore democracy which has been so undermined by the Park government".
South Korean presidential candidate Hong Jun-Pyo, left, prepares to give a speech during a campaign rally in Seoul on May 8.
Mr Hong said the election was a "war of regime choices between people, whether they decide to accept a North Korea-sympathising leftist government or a government that can protect the liberty of the Republic of Korea", South Korea's formal name.
"I'm most anxious about national security and North Korea", said Shim Yeon-sun, who turned up Tuesday to vote for Mr. Hong at a polling station near the lighting store where she works in downtown Seoul.
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Yoo Seong-min of the conservative Righteous Party gained 7.1 percent support, and Sim Sang-jung of the liberal Justice Party had 5.9 percent.
Liam McCarthy-Cotter, a specialist in East Asian politics at Nottingham Trent University, said there was a need for South Korea "to reestablish its strength both domestically and in the face of increasingly hostile posturing from North Korea". "We need a leader who can restore the people's trust in government that was damaged by Park's scandal".
Shortly after impeaching their leader over a huge corruption scandal that rocked the country, South Korea has returned to the poll to vote in a new leader.
Moon says he would want to be approachable and move freely among the people, even though many thought that "unrealistic".
Polls will close at 8 p.m. (1100 GMT), two hours later than in 2012.
Because it is an early election to fill the vacancy created by the termination of Park presidency, the five-year tenure of the new president will begin as soon as the National Election Commission finalizes the victor.
If the rate exceeds 80 percent, it would mark the first time since the presidential election in 1997 that participation has been so high.
The election had been considered tilted in favour of liberal candidates from the very onset as it followed the removal of the former conservative president over corruption allegations. Ahn, a former doctor and computer software mogul, competed with Moon as an independent to be the single candidate representing liberal camps in 2012, but he dropped out at the last minute.
Polls opened at 6am (7am AEST) and will close at 8pm, with exit polls released shortly afterward.
South Korea's election body says almost 64 percent of the country's 42.4 million eligible voters cast their ballots as of 3 p.m. Tuesday, representing a faster pace than the previous presidential election in 2012.
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