Kim Jong Un’s sister “courteously” handed President Moon Jae-in a personal letter from the North Korean leader as the pair met for historic talks at the South Korea Winter Olympics.
North Korea’s delegation to the games will conclude its visit later on Sunday, having appeared to thaw the rift with the South, but there is scepticism about how sincere Pyongyang is about improving relations.
The north’s state-run agency said the talks were “warm” but added they were “frank and candid”. However, the statement made no mention of Mr Kim’s invitation to Moon to a summit “at his earliest convenience”.
Kim Yo Jung, the leader’s sister, also spoke of her brother’s “intention” but did not elaborate on what that was, during the Saturday lunchtime talks.
Mr Moon said in response the two countries should “create the environment for that to be able to happen”.
But both South Korea and the US has been cautious about the talks, saying there will not be progress without North Korea giving up nuclear weapons.
Chang Je-won, a spokesman for Liberty Korea Party, said: “We should firmly keep in mind any talks, where denuclearisation is not a precondition, only buy North Korea more time to complete its nuclear capabilities while they fool us with their peace offensive facade.”
As he left the games, US Vice President Mike Pence said: “There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile programme.”
A White House spokesman added that Mr Moon had told Mr Pence no one would take pressure off North Korea until it takes steps to denuclearisation.
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If a summit does go ahead, it will be the first between the two Koreas since 2007.
Mr Moon and Mr Kim’s sister will have another opportunity to talk when they attend the final performance of a visiting North Korean orchestra on Sunday evening in Seoul.