"We should firmly keep in mind any talks where denuclearisation is not a precondition only buy North Korea more time to complete its nuclear capabilities while they fool us with their peace offensive façade", said Chang Je-won, spokesman for the Liberty Korea Party.
For its part, Japan has made clear that it favors the swift resumption of joint US-South Korean military exercises, which had been put off until after the Olympics in an effort to smooth the path for North Korea's participation at PyeongChang.
The invitation, delivered by Kim's visiting sister Kim Yo Jong, said Kim was willing to meet the South's leader "at the earliest date possible", said a spokesman for the presidential Blue House.
South Korean President Moon Jae (centre) shakes hands with North Korea's Kim Yo-jong (sister of North Korean leader Kim Jong-un) during the Opening Ceremony of the PyeongChang 2018 Winter Olympic Games at the PyeongChang Olympic Stadium in South Korea.
"She (Kim Yo Jong) is not charming, she is a dictator's sister", Laila said."She is not looking after North Korean people".
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.
Moon and Pence spoke Saturday while taking in the speedskating competition, but aides did not immediately say whether the invitation came up during the discussion.
But in a sign Kim Jong-un is unlikely to give up his nuclear arms, he used the day before the Olympics to host a massive military parade which included trucks carrying intercontinental ballistic missiles - weapons that could potentially strike the U.S. mainland.
The two neighboring rival countries displayed an act of solidarity by having some participants from each country honored together during the opening ceremony, and combining the respective women's hockey teams into a singular, unified one. "Moon should be aware that he has to urge denuclearisation to North Korea by himself, not depending on dialogue between the USA and North Korea", an editorial in the Yomiuri Newspaper read.
Moon shook hands with both Kim Yo Jong and Kim Yong Nam at the Olympics opening ceremony and they cheered as athletes from North and South entered the arena together behind a unification flag showing an undivided Korean peninsula. The North Koreans have invited Moon to visit Pyongyang in what would be the third inter-Korean summit talks since their 1945 division.
The organisers of the PyeongChang Winter Olympics said Saturday its servers were hacked by an unidentified attacker during the opening ceremony the previous day. It is one we are dealing with.
It is now unclear how the unidentified Korean man was able to jump the barriers and get onto the ice chute but local police in Pyeongchang, the South Korean resort where the two week tournament is held, say they are investigating.
Kim Ryon Hyang of North Korea, top center, leaves after free skiing on the giant slalom course at the Yongpyong Alpine Center at the 2018 Winter Olympics in Pyeongchang, South Korea, Sunday, Feb. 11, 2018.