Lawmakers from Moon's liberal ruling party have talked about the possibility of South Korea sending a special envoy to Pyongyang to meet with Kim Jong-un.
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.
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 program.
U.S. Defense Secretary Jim Mattis said on Sunday it was too early to tell whether a diplomatic detente between the two Koreas at the Winter Olympics would lead to results, but the move had not driven a wedge between Washington and Seoul.
Saturday's meeting was the first time a South Korean president hosted North Korean officials for a luncheon at the Blue House since November 2007, when late liberal President Roh Moo-hyun, the political mentor of Moon, invited then-North Korean premier Kim Yong Il following a meeting with government officials in Seoul. The first liberal president in a decade, Moon during his inauguration speech a year ago that he would be willing to visit Pyongyang and meet with Kim Jong-un if that helps solve the nuclear problem.
Moon neither accepted nor rejected the invitation, saying "the environment" should be created for such a summit to take place, apparently mindful of the US. It was the only documentation on the table on the North Korean side.More news: Zeid urges worldwide action as violence soars in Syria
"I think this overture towards South Korea is partly sanctions-related, and also related to the fact that it's clear a divergence has developed between Washington and Seoul's most keenly desired goals in the near term", said Andray Abrahamian, a research fellow at Pacific Forum CSIS in Hawaii.
Moon was invited to a summit with Kim, even as the U.S. warned against falling for Pyongyang's Olympic charm offensive. South Korea's presidential Blue House also had no immediate comment.
Moon's desire to engage North Korea was in contrast to his USA ally.
Pence also attended the Games opening ceremony but had no contact with the North Korean delegation.
The two Koreas are still technically at war after the 1950-53 conflict on the Korean peninsula ended in a ceasefire and not a truce.
Take, for example, the following headlines - ones you'd normally expect to find in North Korea's state-run media.More news: 3rd Women's ODI: India lose to South Africa by 7 wickets
North Korean officials refused to meet with any USA representatives after months of tensions between the two countries over the North's nuclear weapons program.
Tensions between the two soared past year as Pyongyang launched intercontinental ballistic missiles capable of reaching the USA mainland and carried out by far its most powerful nuclear test to date.
But analysts say it may be more hard for the South to arrange a summit with the North coming off a year in which Pyongyang test-fired dozens of missiles, including three ICBMs, and conducted its most powerful nuclear test to date.
All relevant parties should make joint efforts to broaden their dialogue channel so as to maintain peace on the Korean Peninsula, a South Korean expert said.
A rare invitation to Pyongyang for South Korea's president marked Day Two of the North Korean Kim dynasty's southern road tour Saturday, part of an accelerating diplomatic thaw that included some Korean liquor over lunch and the shared joy of watching a "unified" Korea team play hockey at the Olympics.
The two Koreas have a rocky and sometimes violent history at the Blue House.More news: Winter Olympics 2018: Snowboarder Jamie Anderson gives Team USA its second gold
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