"They shouted something in Korean, I wasn't sure what it was", he said, "and then the police got involved and they dragged me away - they said for my own safety".
Pence's remarks are in line with Secretary of State Rex Tillerson, who said in December that the USA was ready to talk to the North without preconditions.
With North Korea's self-style "Army of Beauties", a 200-strong band of cheerleaders, erupting in song at every triple twist lift and double axel, the pair earned 124.23 points to beat their previous best of 119.90 for a highest ever total of 193.63.
The prospect of negotiations comes after months of tensions over North Korea's nuclear and missile programs, in which U.S. President Donald Trump and North Korean leader Kim Jong Un traded insults and threats while the United Nations tightened sanctions.
Pence had vowed just days earlier that Washington would not allow North Korea to "hide behind the Olympic banner the reality that they enslave their people and threaten the wider region".
The South Korean government is now considering an invitation from Kim Jong-un to attend a rare summit in Pyongyang.
But despite how close their seats were, officials from the US and North Korea decided not to speak or meet.
North Korea defends its weapons programs as essential to counter USA aggression, saying military drills between the United States and the South are preparations for invasion.
Koo Bon-jae, a 20-year-old student from the South Korean capital, added: "I was initially against it but I was touched after seeing them on the ice together".
Kim Jong Un 'impressed' with South Korea's efforts
Pence told Axios that regardless of the North-South talks, there was "no daylight" between the allies on the need to intensify pressure on Pyongyang. The North has refused to negotiate over its nuclear weapons as it nears its goal of being able to launch an atomic-tipped missile that could strike the US mainland. North Korea conducted its most powerful nuclear test in September amidst worldwide warnings.
"The goal is denuclearization and the process is dialogue for dialogue, action for action, so if North Korea does not show actions, the United States and Japan will not change their policies", a senior Japanese diplomat told lawmakers.
Talk of an inter-Korean summit, which would be the first since 2007 if it happened, come after months of tension between Pyongyang, Seoul and Washington.
The interaction is one of several visible moments of friendship between the North and South Korean athletes, who this year marched under a single "unification flag" at the Olympics opening ceremony.
A Kim Jong-un impersonator has been ejected from the Winter Olympics.
Mr Moon did not immediately accept the North Korean offer.
This is where North Korea would put its nuclear and missile tests on hold in exchange for the scaling down of joint United States and South Korean military drills, said Dr Michell.
In a separate report, KCNA said Kim met members of the Samjiyon Orchestra, which performed in South Korea.