Speaking to reporters later aboard Air Force One, Pence reiterated that there was "no daylight" between the US, South Korea and Japan in pushing to isolate North Korea until Kim abandons his nuclear program.
The United States insisted it would continue its policy of exerting worldwide pressure on North Korea in an effort to get it to abandon its nuclear program.
But US Vice President Mike Pence told Washington Post columnist and CNN political analyst Josh Rogin that he and Moon agreed on terms for further engagement with North Korea, including sitting down with Pyongyang without preconditions.
Moon won't have much space to negotiate with North Korea without backing from the U.S., said Christopher Green, senior adviser on the Korean peninsula at the International Crisis Group in Amsterdam.
US Defense Secretary James Mattis also denied rumblings that North Korea could drive a wedge in Washington and Seoul's relationship.
South Korea said it will seek ways to continue engaging North Korea including trying to arrange more reunions for families divided by the Korean War and aim to lower military tensions.
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But he desperately needs a victory at home to struggling West Brom on Monday to keep Chelsea on track for the top four. But I understand that we have to live with this pressure, and it's OK for me and my players".
On the other, the president of South Korea sat with Kim Jong Un's sister and North Korea's nominal head of state, separated only by International Olympic Committee president Thomas Bach.
Mr Moon and Mr Kim's sister will have another opportunity to talk when they attend the final performance of a visiting North Korean orchestra on Sunday evening in Seoul.
Fred Warmbier accompanied Pence during his visit to South Korea.
The source also described as "undignified behavior" Pence's decision to stay seated and to not applaud the unified Korean team at the opening ceremony, adding that the Vice President "took the low road instead of acting like a big brother".
USA officials have been urging South Korea to be cautious in its rapprochement with the North.
The delegation, the highest-ranking to visit the South and led by the younger sister of the North's leader Kim Jong Un, concluded its visit on Sunday after charming and intriguing the South Korean public, but still faces deep scepticism over Pyongyang's sincerity towards improving relations.
"The president (of the IOC, Thomas Bach, ) nearly as a bridge sat between the president of the Republic of Korea and the honorary head of state of the DPRK last night and they were talking throughout the hockey", Adams said, using the abbreviation for North Korea's official name, the Democratic People's Republic of Korea.
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Holly and Jessica had left a family barbecue to walk to a sweet shop when they vanished. He hid their bodies in his Ford Fiesta before dumping them in woods near RAF Lakenham.
A Blue House official said Moon "practically accepted" the invitation.
Kim Yo Jong and Kim Yong Nam arrived Friday afternoon, leading a senior delegation.
Pence, who was in South Korea for the Olympics, has said the United States and South Korea were closely aligned in their approach to dealing with North Korea. The U.S. has said it would accept dialogue with the North if it shows willingness to give up its nuclear weapons program.
In the next heat, when South Korea star skater Lim Hyojun was up, they put down their home country flags and waved the white and blue unification flags that were introduced at Friday night's Opening Ceremony at the Olympic Stadium in Pyeongchang.
Mr. Han, however, is not convinced it means anything, saying what North Korea wants most is to reduce pain from worldwide sanctions.
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Sometimes I take that decision and of course the prestigious pundit can say whatever he wants. "It's so serious. He claimed he did not have enough fit first-team stars and his youth players had already played that weekend.