Pence met with Moon later Thursday, and both reaffirmed a principle of "using maximum sanctions and pressure to bring North Korea to the negotiating table for denuclearization", said Moon's spokesman, Yoon Young-chan.
Pence declined to offer specifics on exactly what the new package of sanctions would consist of.
North Korea has no intention to meet USA officials during the Winter Olympics in the South, Pyongyang's state media has said, but did not rule it out.
Shortly before Pence made his announcement in Tokyo, South Korea's Unification Ministry announced that Kim Jong-un, the supreme leader of North Korea, planned to send his sister, Kim Yo-jong, as part of the North's high-level delegation to the Olympic Games.
Although the USA had not requested talks with North Korea, Mr Pence left open the possibility of some contact.
The North Koreans' trip has raised hopes within Moon's government, which has sought to use the North's participation in the Olympics to expand dialogue with North Korea and ease tensions over the North's nuclear weapons program.
Off in the distance, North Korea's flag was high in the air, flying above the propaganda village.
Before leaving Japan for Korea, Pence announced that the US would unveil in coming days "the toughest and most aggressive round of economic sanctions on North Korea ever".
But the North's KCNA news agency reported a senior foreign ministry official as saying: "We have never begged for dialogue with the United States nor in the future, too".
(Nexstar) - A bus took reporters deep into the demilitarized zone that divides North and South Korea.
"By sending key figures like his sister, Kim Jong Un is aiming to send a signal to the South that it is giving more weight to inter-Korean ties while driving a wedge between South Korea and the United States", said Kim Sung-han, a former South Korean vice foreign minister. "There is no need to do so".
Pence told reporters that despite disagreements over how to approach North Korea, the state of the alliance between the USA and South Korea is "strong".
"We'll continue to seize every opportunity to ensure that North Korea does not use the powerful imagery and backdrop of the Olympics to paper over an appalling record of human rights and a pattern of developing weapons and conducting the kind of missile launches that are threatening our nation and threatening neighbors across the region", Pence said.
"Explicitly speaking, we have no intention to meet with the USA side during the stay in South Korea". North Korea held a parade highlighted by intercontinental ballistic missiles one day before South Korea hosts the opening ceremony of the Winter Olympics. "But we'll see what happens".