The White House issued a statement after a North Korean delegation to the neighbouring South reportedly expressed willingness to talk to Washington, amid a longstanding nuclear standoff with Pyongyang that has raised fears of a devastating atomic exchange.
The group ended a three-day visit to the South in which it repeatedly expressed its willingness to talk with the USA, reports Efe news.
Moon met Kim in Pyeongchang, where the Olympics were held, before the closing ceremony, the South Korean government said.
North Korea - which carried out multiple missile tests previous year, including those believed capable of reaching the United States mainland - has long expressed its desire to talk to Washington without preconditions.
The Olympics gave a boost to recent engagement between the two Koreas after more than a year of sharply rising tensions over the North's missile program and its sixth and largest nuclear test in defiance of United Nations sanctions.
The White House said its sanctions would continue.
A North Korean envoy sent a message through South Korea on Sunday saying the North has "ample intentions" of holding talks with the U.S.
Moon, who advocates dialogue with the North to defuse tension, said yesterday that Washington needs to "lower the threshold for talks" with the North.
But it was too early to take the North's comments as a major breakthrough. Hong Joon-pyo, the leader of the conservative opposition Liberty Korea Party, said during the protest.
Kim Jong Un's sister, Kim Yo Jong, attended the opening ceremony in an historic first no member of the ruling Kim family had ever traveled to the South before. They did not speak.
Kim is suspected of masterminding and ordering the attack on South Korea's Cheonan warship in 2010, which sank and left 46 people dead. The North Korean leader later said he wanted to boost a "warm climate of reconciliation and dialogue".
The North's state-run news agency ran a story Sunday quoting a "spokesman for the Korea Asia-Pacific Peace Committee" as saying that Pence insulted Kim's sister with his hard-line rhetoric after returning to the USA and "we will never have face-to-face talks with them even after 100 years or 200 years".
"Both sides agreed to work together for permanent peace on the Korean peninsula, sustainable relations between North and South Korea and balanced cooperation with the global society", the South's presidential office said in a statement. "North Korean relations should be improved together", the statement said.
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