Yet the two sides disagreed when South Korea proposed talks on denuclearization, with North Korea issuing a "strong complaint" that Seoul would raise that point.
The South Korean delegation, for its part, proposed North Korea send a big delegation and conduct a joint march during the February 9-25 Game's opening and closing ceremonies, Chun, one of the five South Korean negotiators, said.
China - the North's major diplomatic backer and trade partner - and Russian Federation, with which it also has strong ties, both welcomed the inter-Korea talks.
South Korea said on Tuesday it will consider a temporary lifting of sanctions against North Korea if it is necessary to facilitate the visit of North Koreans to the Winter Olympics in South Korea next month.
South Korea, he said, wants to pursue denuclearization without risking a devastating war with North Korea that would put at risk millions of Koreans on both sides of the border. The South Korean delegation, sporting the national flag and Pyeongchang Olympics on their badges, appeared to have more files in their bags than their counterparts.
Trump had been critical of the prospect of negotiating with the North Korean leadership that has broken past agreements to end its nuclear program in exchange for economic assistance and security guarantees.
Al Jazeera's Florence Looi reports from Seoul.
Seoul said the talks could eventually lead to a "fundamental resolution" of the nuclear threat on the peninsula.
Kim raised the possibility of starting the talks in a New Year's Day speech.
US President Donald Trump has a much closer relationship with Japanese Prime Minister Shinzo Abe than he does with Moon, and has claimed credit for the North-South talks.
South Korean President Moon Jae-in's first New Year's news conference before some two hundred Korean and foreign press televised live across the nation. "And so, we remain focused on our global pressure campaign".
Trump and Kim traded bellicose warlike rhetoric and even crude insults a year ago, as the North conducted it sixth and most powerful nuclear detonation and three tests of intercontinental ballistic missiles.
Seoul will also freeze the $8 million Tokyo donation to the Comfort Women and instead use South Korean government funds to help the survivors.