Sweden has had diplomatic relations with North Korea since 1973 and is one of the few Western countries with an embassy in Pyongyang.
North Korea's state media has yet to comment on the content of Kim's meeting with the South Koreans, but North Korean Foreign Minister Ri Yong Ho arrived in Sweden this week for talks with his Swedish counterpart Margot Wallstrom, prompting speculation he could lay the groundwork for a Trump-Kim summit.
Trump rattled the global community and his own administration last week when he quickly accepted North Korea leader Kim Jong Un 's invitation to meet.
The visit marks the reclusive nation's first major diplomatic overture since President Trump said he'd consider meeting North Korea's leader Kim Jong Un.
South Korea will seek high-level talks with North Korea this month as preparations for a summit began on Friday, the presidential chief of staff said, while officials in the South expressed interest in a separate summit with the United States.
While the White House has spoken openly about Trump's plans to meet with Kim, including discussion of preconditions that were not initially included in the president's announcement, North Korea has been uncharacteristically silent on the meeting.
Sweden has played a neutral role between the USA and North Korea in the past.
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Sweden has said it is ready to act as a facilitator to help resolve tensions on the Korean peninsula.
Trump fired Tillerson on Tuesday, and picked CIA Director Mike Pompeo as his replacement.
Trump also doesn't realize that China and Russian Federation are our real enemies and that US presidents don't personally negotiate with murderous madmen.
Kang held talks later on Friday with Sullivan, who is standing in after Trump fired Rex Tillerson as USA secretary of state this week.
The Japanese and South Korean ministers were expected to meet in Washington on Saturday.
Admiral Harry Harris told the U.S. Senate Armed Services Committee he believed the United States would stick to its demand for the "complete, verifiable, irreversible denuclearisation" of the Korean peninsula.