A senior administration official said Moon did express to the vice president that he hoped there could be some potential interaction between Pence and the North Korean delegations during the games - something that did not occur.
"I am very confident, as President Trump is, that President Moon will continue to stand strongly with us in our extreme-pressure campaign", Pence told NBC in an interview, maintaining all options were open to deal with the crisis.
Following the talks, South Korean officials said Kim Yo-jong had invited Mr Moon to visit Pyongyang.
Before the ceremony, South Korean officials released a statement from President Moon Jae-in. These officials said that while Pence did not greet Kim Yong Nam, he didn't deliberately skip over him.
While President Trump and Vice President Pence proceed to use severe rhetoric when discussing relations with North Korea, the governments of the two Koreas are continuing to take diplomatic steps to ease tensions that have existed between them for decades.
But the prospect could sow division between the dovish leader, who has long argued for engagement with the nuclear-armed North to bring it to the negotiating table, and US President Donald Trump, who a year ago traded personal insults and threats of war with Kim.
Some South Korean media had criticized Pence's decision to attend the opening reception for only five minutes, instead of sitting at the same table as the North Koreans, and not to stand when the joint Korean team entered the stadium on opening night. However, he did not meet with Yong-nam and Yo-jong.
As if to drive the point home, Kim Jong-un used the eve of the Olympics to throw a massive military parade in Pyongyang that was highlighted by several huge intercontinental ballistic missiles rolled out in launcher trucks. They stressed the North Koreans in the VIP box had watched Pence, Moon and Abe hold a running discussion in the front row for the more than two-hour ceremonies. Communications director Jarrod Agen tweeted a laudatory review of Pence's evening: "VP stands and cheers for USA athletes".
North and South Korea are technically still at war after their 1950-1953 conflict ended in a truce rather than a peace treaty.
Spicing up political rapprochement, North Korean cheerleaders and South Korean spectators rooted together for the joint women's ice hockey team in its first match at the PyeongChang Winter Olympic Games on Saturday. Kim's sister, Kim Yo-jong, personally delivered the message as she was in Seoul for the Winter Olympics.
But North Korea's awful record on human rights and the growing threat from its nuclear weapons program appeared out of mind.
Sunday's KCNA report cited Moon as saying inter-Korean relations should be mended by the parties concerned "at any cost as indicated by Chairman Kim Jong Un in his New Year Address".
Many experts say Kim's overture is meant to use improved ties with Seoul as a way to weaken US -led global sanctions toughened after its series of big weapons tests previous year that include its sixth and largest nuclear test explosion and three intercontinental ballistic missile launches.
Both of those South Korean presidents had struggled under growing domestic criticism after their trips to Pyongyang had resulted in large shipments of aid and investment but failed to end the North's nuclear weapons program.
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