And while Moon could not miss the chance to "lower the temperature in the room" by engaging with Kim during her visit for the Olympics, her public relations blitz could subject the South Korean president to criticism that "he fell for a charm offensive", Kang said.
Nothing has been settled on any trip north by South Korean President Moon Jae-in.
Moon asked the North Korean delegation during Saturday's meeting to engage in dialogue with Washington "at an early date", the Blue House said.
In January 1968, Kim Yo Jong's grandfather, founding North Korean president Kim Il Sung, sent a squad of North Korean commandos to Seoul who tried unsuccessfully to kill then-president Park Chung-hee.
US Vice President Mike Pence, also in South Korea for the Olympics, has said the United States and South Korea were closely aligned in their approach to dealing with North Korea.
The North Korean delegation arrived in the South on Kim's private plane on Friday via Incheon worldwide airport to attend the opening ceremony of the Pyongchang Winter Olympics where Seoul and Pyongyang are represented by joint teams.
But it could threaten to sow division between Moon, who has long argued for engagement with the nuclear-armed North to bring it to the negotiating table, and US President Donald Trump, who a year ago traded personal insults and threats of war with Kim.
A visit by Moon to the North would be only the third inter-Korean summit to take place.
"I never thought I would visit (the South) so suddenly and believed much would be odd and different but I saw many things that were similar or the same", said Kim Yo Jong in a toast during Sunday's dinner, adding she hoped to meet the "friendly faces" before her later in Pyongyang.
The recent detente, anchored by South Korea's hosting of the Winter Olympic Games that began on Friday, came despite an acceleration in the North's weapons programs a year ago and pressure from Seoul's allies in Washington.
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It was very rare for a South Korean president to hold formal talks with high-ranking North Korean officials, as the two countries remain technically at war after an armistice stopped the 1950-53 Korean War.
Kim Yo-jong with North Korea's nominal head of state Kim Yong-nam. The North Korean orchestra will return home on Monday after their second and last performance on Sunday.
Kim Eui-kyeom, South Korean president's spokesman, said at a news conference in Seoul on Saturday that the North Korean delegation delievered the invitation letter at a landmark high-level meeting at the presidential palace in Seoul.
"The inter-Korean relations should be mended by the parties concerned at any cost", Moon was quoted by the agency as adding.
During Sunday's lunch at the Walkerhill Hotel, Prime Minister Lee told the North Korean delegation he hoped the "right conditions" would be created for the two heads of state to meet, an official from Lee's office said.
The event, cheered by the crowd at the Gangwon Career Education Institute in Sokcho, featured teams from both countries performing for 25 minutes before briefly joining together as one.
South Korea suggested the formation of a joint team as part of its efforts to use the Games to re-engage with the North and pave the way for talks over the North's weapons programme.
Japanese editorials sounded a similar warning, saying dialogue would be meaningless unless it led to denuclearisation of the Korean peninsula.
"What can not be overlooked is that Moon did not directly demand North Korea to abandon its nuclear development".
Moon did not immediately accept the offer, calling instead for efforts to "create the right conditions to realise" such a visit and urging Pyongyang to actively seek dialogue with the United States, he added.