South Korea President Moon Jae-in, who hopes to use these Games as an opportunity to engage with the North, warmly greeted U.S. President Donald Trump's daughter Ivanka before offering a brief handshake to North Korean delegation leader Kim Yong Chol.
The Pyongyang delegation said developments in relations between the two Koreas and between North Korea and the United States should go hand in hand, according to the statement.
Gen Kim and Mr Moon both watched the closing ceremony of the "Peace Games" and shared a brief handshake in a VIP box in which US President Donald Trump's daughter, Ivanka, and the top US military commander on the peninsula, General Vincent Brooks, also Saturday.
Bach signed off by calling upon the youth of the world to gather in Beijing in four years' time for the 2022 Winter Games.
The North Korean delegation, led by former military intelligence chief Kim Yong Chol, met Chung Eui-yong, security adviser for the presidential Blue House, and other South Korean government officials for lunch on Monday.
South Korea's President Moon has tried to bring Washington and Pyongyang together at these Olympics. But Koh Yu-hwan, a professor of North Korean studies at Dongguk University in Seoul, said that North Korea's primary strategy was not to avoid sanctions but to get the United States to accept it as a nuclear weapons state in return for a freeze on its nuclear program.
North Korean leader Kim Jong Un indicates he may be receptive to taking part in talks with the U.S.More news: Harvey Weinstein Casting Couch Statue Surfaces By Oscars Venue
In order to broker talks between the two sides, the South Korean leader is "working hard with sincerity" with a posture of "maximum prudence", according to Moon.
But experts say arranging an inter-Korean summit would be hard after a year in which North Korea conducted its most powerful nuclear test and flight-tested intercontinental ballistic missiles that could, when perfected, target the US mainland.
North Korea previous year increased the pace of its missile programme.
Both the US and South Korean responses come a day after North Korean officials said they are willing to sit down with representatives from the US.
"If we can make a joint road map that provides a reasonable incentives for the North, Pyongyang could be persuaded", he said. Ivanka Trump, who was leading the USA delegation, briefed Moon on the latest set of sanctions and delivered a personal message from her father after she arrived in Seoul on Friday for her four-day visit.
The possible thaw comes amid a backdrop of a series of ever-toughening sanctions against the North, spearheaded by the United States, as recently as last week.
While Kim reiterated his statement that North Korea was open to dialogue with the United States, its archenemy, he did not exactly welcome the idea of talking about denuclearization.