When asked whether the secretary general had any contact with Kim Jong Un's sister, Kim Yo-jong, the spokesman replied that their direct communication was unlikely.
South Korea says the artists will return to the North on Tuesday by a land route.
North Korea has spent years developing its military, saying it needs to protect itself from US aggression.
Providing fuel to the ferry would have been a hard decision for Seoul because of concerns that North Korea is trying to use the Olympics to poke holes in worldwide sanctions against the country over its nuclear and missile programs.
Pyongyang has ruled out a meeting with the USA delegation during the Winter Games.
Tensions between the two soared a year ago as Pyongyang launched intercontinental ballistic missiles capable of reaching the USA mainland and carried out by far its most powerful nuclear test to date.
Even so, there's also cautious optimism, or curiosity at least.
It was already known that Kim Yo Jong is an adviser to her brother; now many are interpreting her presence here - and the freedom with which she seems to behave - as new signs of the power she holds.
Kim's younger sister, Kim Yo-jong, handed the letter over at a rare meeting with Moon on Saturday. US and Japanese press initially photographed the two without Moon.
Mr Pence has repeatedly left open the possibility of an encounter at the Games, but said the USA had not requested a meeting. The South Koreans want to use the Olympics to ease tensions spurred by North Korea's pursuit of nuclear weapons.
In addition to Moon and Kim's sister Kim Yo Jong, the game was attended by Kim Yong Nam, North Korean titular head of state, and International Olympic Committee (IOC) President Thomas Bach.
The younger Kim met and had lunch with Moon at the presidential complex as a special envoy of the DPRK leader.
The opening part of the talks was mostly about the weather: Pyeongchang was colder than Seoul, it was agreed.
The figures from the two Koreas shared kimchi (Korean pickled cabbage) and soju rice liquor, and spoke for three hours.
The attendance of North Korean athletes, which followed a flurry of diplomacy in January and February, was just the tip of the iceberg, however.
Born in 1987, she studied in Switzerland, like Kim Jong Un, and is believed to have attended Kim Il Sung University and a European school for her higher education. She said it's been an easy adjustment all around. Officials didn't reveal what was written in it. And women's ice hockey players from both Koreas will compete as one team. The Swiss won 8-0.
Pence's office didn't directly address Kim's invitation to Moon.
"President Moon and President Trump are completely aligned in their objective for a nuclear free Korean Peninsula", Pence said.
The cool USA attitude toward the North Korean presence at PyeongChang, contrasted with Moon's enthusiasm, has sparked discussion of a growing divide between the allies over how to approach Pyongyang.
Pence said Friday that the US would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
Not to be overlooked is that Moon did not directly demand the North abandon its nuclear development programs.
The son of North Korean refugees and a leading advocate of a previous liberal government's "Sunshine Policy" of engagement with the North, Moon has spent his career - a lifetime, really - waiting for this chance. It has only deepened over the years as the North closes in on the ability to field an arsenal of nukes that can hit USA cities.
Some people tried to burn the North Korean national flag, but were contained by police.
In South Korea and beyond, commentators are taken with Kim's surprisingly stylish and relaxed demeanor.
Even if there are more meetings between the rivals after the Games, accomplishing something is another matter.
A selfie unites figure skaters from North and South Korea.
United Nations deputy spokesman Farhan Haq told reporters at United Nations headquarters that Guterres sat near 90-year-old Kim Yong Nam at a dinner Friday night, and they were also near each other during the opening ceremony of the Winter Olympics in Pyeongchang. Pence carried a similar message. Roh continued the efforts, which saw North and South Korea pursue now-stalled economic cooperation projects and reunions of families separated since the 1950-53 Korean War, which ended with an armistice, not a peace treaty.