The official said Pence and Moon did not discuss the North Koreans' invitation to Moon for a summit in Pyongyang, which would set the stage for the first meeting of Korean leaders in 10 years.
During Saturday's meeting, Moon also called for the North to step forward to engage in talks with the U.S.
The recent detente, anchored by South Korea's hosting of the Winter Olympic Games that began on Friday, came despite an acceleration in the North's weapons programs a year ago and pressure from Seoul's allies in Washington.
The Korean Central News Agency reported that Kim Yo Jong delivered a letter and message from her brother during the meeting Saturday in Seoul, but did not mention that Kim Jong Un invited Moon to visit Pyongyang for a summit.
The South Korean leader said in response "let's create the environment for that to be able to happen", Blue House spokesman Kim Eui-kyeom told a news briefing.
In stark contrast, two kinds of kimchi - the fermented cabbage that features in every Korean meal - were on the menu for the delegation's lunch with Moon at the Blue House on Saturday, one mild Northern style version and a spicier Southern recipe, along with soju, the traditional Korean rice liquor.
"We would like to see you at an early date in Pyongyang", Kim Yo Jong told Moon during the lunch, according to another Blue House official.
The North has sent almost 500 people to the Pyeongchang Games, including officials, athletes, artists and also a 230-member state-trained cheering group after the Koreas agreed to a series of conciliatory gestures for the games.
"Moon is saying that although he is keen to reboot inter-Korean relations, the dialogue between the United States and the North is essential". But the North Korean cheerleading squad there to support the team? Analysts say that the missiles, which were successfully flight tested three times past year, could potentially reach deep into the US mainland when perfected.
President Donald Trump's administration has taken a hard line on North Korea's nuclear and ballistic missile programme, saying there is no room for negotiations unless Pyongyang abandons it.
"I'm announcing today that the United States of America will soon unveil the toughest and most aggressive round of economic sanctions on North Korea ever", Pence said.
The two Koreas have been divided since the conflict ended in a ceasefire in 1953, and the democratic South has risen to become the world's 11th-largest economy, while the North has stagnated under the Kim family's rule.
North Korea has spent years developing its military, saying it needs to protect itself from U.S. aggression.
Moon has expressed his intention to use the Winter Olympics as a chance to make diplomatic inroads with the North and restore normalcy, following months of high tensions on the Peninsula.
The delegation, which includes Kim's sister, Kim Yo-jong, is in South Korea for the Winter Olympics.
He also did not shake hands with Kim Yong Nam while making a brief appearance at a leaders' reception ahead of the ceremony - although Japanese Prime Minister Shinzo Abe, whose country is also regularly threatened by Pyongyang, did so, while exchanging pleasantries with the North Korean.
It was very rare for a South Korean president to hold formal talks with high-ranking North Korean officials, as the two countries remain technically at war after an armistice stopped the 1950-53 Korean War.
They were on both sides of the ice, chanting back and forth.
The unified hockey team representing North Korea and South Korea didn't fare so well in their first outing, losing 8-0 to Switzerland.
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