According to reports, Ms Kim left a note at the palace expressing hope that "Pyongyang and Seoul will become closer in the heart of Koreans" and for "unification and prosperity in the near future".
Mr Moon's spokesman Kim Eui-kyeom said that Mr Kim's sister verbally delivered his offer during a lunch meeting with Mr Moon at Seoul's presidential palace.
"There is no daylight between the United States, the Republic of Korea, and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear ballistic missile program", Pence said in comments carried by CNN.
Kim Yo Jong has been an increasingly prominent figure in North Korea's leadership and is considered one of the few people who has earned Kim Jong Un's absolute trust.
The first summit was in June 2000 between Kim Dae-jung, a proponent of the so-called Sunshine Policy, and Kim Jong Il. In January, South Korea's decision to allow the North's teams to compete in this year's Olympic games in Pyeongchang was a historic step toward diplomacy.
USA officials have remained suspicious over Kim's intentions as the North cosies up to the South over the Olympics.
Domestic tourists 'scum of earth': Goa minister Vijai Sardesai
Claiming that he was quoted out of context, the Goa minister said that he referred to only a "certain section of them, not all". Sardesai's remarks came during the Goa BizFest in Bambolim, attended by top industrial and tourism sector players of the state.