The response was seen as meaning that there should first be progress on efforts to resolve the North Korean nuclear standoff, such as talks between the United Sates and the North, before what would be a third inter-Korean summit takes place.
Kim Yo Jong, the younger sister of Kim Jong Un, "courteously" handed over a personal letter from the North Korean leader to Moon during talks on Saturday and also told Moon of her brother's "intention", KCNA said, without elaborating on what that was.
Visiting US Vice President Mike Pence did not engage with the North Korean representatives just a few seats away at the opening ceremony, and did not get up to cheer when athletes from the host nation and its neighbour entered the arena together behind a unification flag.
The spokesman said Moon also called for a quick resumption of dialogue between the United States and North Korea.
A White House official said although Moon did not discuss the invitation to Pyongyang with Mr Pence, the South Korean president made it very clear that only when North Korea actually starts to take steps to denuclearise would anyone even consider beginning to take the pressure off.
In Pyongyang, North Korea's official Rodong Sinmun newspaper also reported on the Games bonhomie, publishing photos of its ceremonial head of state clinking glasses with Moon and of the South's leader also shaking hands with a telegenic Kim Yo Jong.
South Korean presidents Kim Dae-jung and Roh Moo-hyun went to Pyongyang in 2000 and 2007 respectively to meet the current leader's father and predecessor Kim Jong Il.
Pakistan's human right activist Asma Jahangir passes away
Jahangir always raised her voice against human rights violations and was a staunch supporter of democracy. She was also the co-founder of the Human Rights Commission of Pakistan and the Women's Action Forum.
The recent detente, anchored by South Korea's hosting of the Winter Olympic Games, came despite an acceleration in the North's weapons programme a year ago and pressure from Seoul's allies in Washington.
Any meeting would represent a diplomatic coup for Moon, who swept to power past year on a policy of engaging more with the reclusive North and has pushed for a diplomatic solution to the standoff over North Korea's nuclear and missile programme.
Pence spent the days leading up to the Pyeongchang Olympics warning that the North was trying to "hijack the message and imagery" of the event with its "propaganda".
North Korea has spent years developing its military, saying it needs to protect itself from US aggression. Pence carried a similar message during his trip to Japan and South Korea.
A senior Japanese defence official said North Korea's Games charm offensive could "simply be a way to gain time" until it completed its nuclear and ballistic missile development.
Pence said Friday the US would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
North Korean media lauded the players and supporters of the unified Korean women's ice hockey team on Sunday after their first match at the Olympics - without mentioning their 0-8 drubbing.
Kim Jong Un invites South's Moon to Pyongyang: Seoul
Moon has said in the past that he only wanted to meet the North Korean leader if they can make progress on nuclear issues. The visual was important, a USA official said.
Demonstrating a non-committal stance, Moon said about the invitation that he wants to "create the environment for that to be able to happen".
But Kelly did not expect the alliance between Washington - which has 28,500 troops stationed in the South to defend it from the North - and Seoul to be put at risk.
"What can not be overlooked is that Moon did not directly demand North Korea to abandon its nuclear development".
The North is a notoriously tough negotiator, adamant that it needs its "treasured sword" of nuclear weapons to defend itself against the threat of invasion by the United States, and will never give them up.
Kim Yo Jong, sister of North Korean leader Kim Jong Un, arrives at the Incheon International Airport in Incheon, South Korea.
The latest North Korean diplomatic overture does not appear to have discouraged Washington from pursuing its strategy of pressure.
Netanyahu speaks to Russia's Putin about Iran
If Israel became more militarily involved in the conflict, what would it mean for the Syrian war - and the wider region? The military says it is "ready for various scenarios and will continue to act according to situation assessments".
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