Lookalikes of Donald Trump and Kim Jong Un who caused a stir at Friday's Pyeongchang Olympics opening ceremony have thanked organisers for their tender loving care.
Moon's spokesman Kim Eui-kyeom said Saturday Kim's sister verbally delivered his offer in a lunch meeting with Moon at Seoul's presidential palace.
The sight of North and South Koreans marching together for the first time in a decade was the culmination of months of work by Seoul.
The South is still technically at war with the North after the 1950-53 Korean War ended in a truce, and the United States and North Korea have recently swapped nuclear threats.
North Korean leader Kim Jong Un (left) and President of the Presidium of the Supreme People's Assembly of North Korea Kim Yong Nam (right) during a military parade in Pyongyang on April 15, 2012.
The meeting could be a prelude to a summit between leaders from the two countries, and Moon has already said he is willing to travel to Pyongyang to meet Kim Jong-un.
Some North Korean experts believe tough United Nations sanctions that are cutting off most of the isolated North's sources of revenue have added pressure on Pyongyang to engage further with Seoul.
Cyber-security teams and experts from South Korea's defence ministry, plus four other ministries, formed part of a taskforce investigating the shutdown, they said, adding that it didn't affect the high-tech opening ceremony.
A senior administration official aboard Pence's airplane also told reporters that South Korea and Japan "are solidly with our alliance and the need to continue and intensify economic sanctions".
"We wanted the North Koreans to see the vice president, Abe and Moon sitting directly in front of them for the opening ceremonies, and it would show that that alliance is strong".
A Blue House official said Moon "practically accepted" the invitation.
A visit by Moon to the North would enable the first summit between leaders from the two Koreas since 2007. Yonhap via REUTERSErin Hamlin of USA carries the national flag.
Although South Korea has been a trenchant supporter of Trump's campaign of "maximum pressure" against North Korea, Moon has been keen to use the Olympics to pry open the door to better relations with its adversary.
Throw in there the accusations that South Korea has had to arrange huge payouts for past meetings, and that these earlier encounters, while producing indelible images, have done little to slow North Korea's pursuit of nuclear weapons.
Kim Yo Jong and Kim Yong Nam are on an unprecedented visit to South Korea amid abrupt reconciliation mood between the rival Koreas for the Pyeongchang Winter Olympics.
"It seems clear", he said, "that the countries have entered a phase of restoring a regular level of contact".
