The meeting, the first of its kind in about two years, was arranged after North Korean leader Kim Jong Un made an abrupt push for improved ties with South Korea following a year of elevated tensions with the outside world over his expanding nuclear and missile programmes.
Critics say Kim may be trying to divide Seoul and Washington in a bid to weaken international pressure and sanctions on the North.
North Korea is weak in winter sports and a pair of figure skaters, Ryom Tae Ok and Kim Ju Sik, earlier became the only North Korean athletes to qualify for next month's Pyeongchang Games before the North missed a confirmation deadline.
The International Olympic Committee said yesterday it has "kept the door open" for North Korea to take part in the games.
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He said South Korea also suggested resuming temporary reunions of families separated by war and offered military talks designed to reduce animosities in front-line areas.
South Korea also stressed the need to achieve denuclearisation of the Korean Peninsula, Chun said.
North Korea responded by saying the two Koreas must try to promote peace and reconciliation through dialogue, he said.
The two sides' chief delegates were meeting yesterday evening to discuss the wording of a joint statement, the media reports said, but it wasn't immediately known when the talks would end. Past inter-Korean talks have often continued until late at night.
The meeting's venue, Panmunjom, is the only place on the tense border where North and South Korean soldiers are just meters (feet) away from each other.
A North Korean soldier in November defected to the South across Panmunjom amid a hail of bullets fired by his comrades. He was hit five times but survived.
Later today, Chun said North Korea told the South Korean delegation that it restored a military hotline with the South, in the second reopening of a suspended inter-Korean communication channel in about a week.
All major inter-Korean communication channels had been shut down amid animosities over the North's nuclear program in recent years. But North Korea reopened one of the channels last week as signs emerged of improving ties.
North Korea is expected to demand rewards in return for South Korea's proposal of family reunions and military talks, such as a halt to South Korean propaganda broadcasts and a scaling back or halting of military drills with the US, observers say.
Suspension of the military drills would be unacceptable for Seoul because it would seriously undermine its alliance with its chief ally, the United States, which wants to put more pressure on North Korea. The North views the drills as a rehearsal for an invasion.
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