Ri held talks late on Thursday with his Swedish counterpart Margot Wallstrom, discussions that according to Swedish officials were to focus on the denuclearisation of the Korean peninsula and a possible Trump-Kim summit.
North Korea's foreign minister met briefly with Sweden's prime minister Friday during a surprise trip to Stockholm that has fueled speculation about a possible meeting in the Scandinavian country between U.S. President Donald Trump and North Korean leader Kim Jong Un.
"We believe in dialogue and in a political process", Wallstrom told reporters.
The talks about talks come after the head of the U.S. Pacific Command said the United States could not be overly optimistic about the outcome of any summit between U.S. President Donald Trump and Kim, aimed at ending the North's nuclear and missile programmes, and must go into it with "eyes wide open".
Sweden has an embassy in Pyongyang, which also represents United States interests in North Korea.
The building is close to the embassies of South Korea and the US.
Swedish public broadcaster SVT reported, without citing sources, that Ri planned to stay in Sweden until Sunday.
Ri was originally scheduled to leave on Friday, but has now made a decision to stay for more talks through Sunday, according to SVT Nyheter. "It is up to the parties to decide how to move forward", Wallstrom said Friday before meeting Ri.More news: Russian Federation retaliates in escalating feud over United Kingdom nerve agent attack
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Before a date or a venue for the summit can be set, North Korea will have to publicly confirm that it sent the invitation and intends to honour it, by attending a meeting to discuss giving up its nuclear arsenal.
The talks in Stockholm will also involve Sweden's consular responsibilities in North Korea, which include representing United States diplomatic interests.
South Korea diplomats said North Korea has agreed to discuss "denuclearization" at the talks, planned for May, though the hermit kingdom has long demanded a removal of USA troops in its southern neighbor in exchange.
South Korean-born Yun, a strong advocate for engagement with Pyongyang, led contact with North Korea and quietly pursued direct diplomacy since taking his post under former President Barack Obama in 2016.
Trump and Moon expressed "cautious optimism" that North Korea could enjoy a "brighter future" after the summit, which is being eyed before the end of May.
He said that the talks between Trump and Kim would only be successful if there are no preconditions.
The isolated state has always maintained it will continue to develop its nuclear weapons as a deterrent against US aggression but, according to South Korea, it later said it was open to abandoning the programme if the security of its regime was guaranteed.