Sweden is among a number of countries touted as a possible venue for what would be a historic meeting between Trump and Kim, who have engaged in bellicose mudslinging over North Korea's nuclear ambitions.
North Korean Foreign Minister Ri Yong Ho was on Thursday en route to Sweden, which represents US interests in Pyongyang, for talks with his Swedish counterpart Margot Wallstrom, the Scandinavian country's Foreign Ministry said.
The historically neutral European country, whose embassy represents USA interests in the North Korean capital, has often played the role of intermediary in discussions between Washington and Pyongyang. It provides consular services for the United States in North Korea.
"They will also address the security situation on the Korean peninsula, which is high on the (UN) Security Council agenda", a ministry statement said.
The discussions between Ri and Wallstrom are to "focus on Sweden's consular responsibilities as a protecting power for the United States, Canada and Australia", the Swedish government said when the two-day visit was announced.
It is one of the few western states with a diplomatic channel to the North Korean leadership and may be able to smooth out obstacles in the path of a summit meeting.
"If the key actors want Sweden to play a role, facilitate (talks), be a forum or a link or whatever it may be, then we are prepared to do that", Prime Minister Stefan Lofven told Sweden's TT news agency earlier Thursday. But we're not naive, we don't think we can solve the world's problems.
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Talks between Sweden and North Korea in Stockholm will continue on Saturday after initially being due to end late on Friday, a source with knowledge of the situation said.
Since Trump's surprise announcement last week that he was willing to meet Kim, speculation has mounted over what location might be chosen to host what would be the first-ever meeting between serving leaders of the two countries.
Ri Yong Ho arrived in the Swedish capital on Thursday evening with Choe Kang Il, deputy director general of the foreign ministry's North America section.
"We'll see what happens next", Wallstrom said.
Meanwhile, Swedish public broadcaster SVT said the Stockholm International Peace Research Institute (SIPRI) was involved in the talks, though SIPRI did not return AFP's calls for a comment.
It could suggest a potential breakthrough, or a fallback to the North's longstanding position that it's willing to get rid of its nuclear weapons if the United States guarantees its safety.
The diplomatic wheels started turning rapidly at the beginning of the year when the two Koreas worked to bring a handful of athletes from the North to compete in the Winter Olympics in South Korea.