Further Moon Jae-in on various occasions had called for re-approachment of six-nation denuclearisation, including South and North Korea, China, Japan, US, and Russian Federation.
As Washington does not have diplomatic ties with Pyongyang, Sweden has represented the United States in North Korea and has often played an intermediary role between the two countries.
Kang's arrival in Washington came just 48 hours after President Donald Trump fired his secretary of state, Rex Tillerson.
"I explained to Secretary Ross that South Korean steel does not pose a threat to U.S. national security and emphasized that the South Korea-U.S. alliance is at a juncture where we need to cooperate", Kang said.
Sweden is now a non-permanent member of the United Nations Security Council.
"We'll see what happens next", Wallstrom said, the Associated Press reported.
According to Daily Mail UK, the announcement was made after North Korea's foreign minister Ri Yong Ho arrived in Stockholm to discuss with the Swedish authorities and pave the way for the much-awaited #Summit Meeting.
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Foreign Minister Ri, who took his post in May 2016, is fluent in English and previously served as North Korean ambassador to London.
Swedish public broadcaster SVT meanwhile said the Stockholm International Peace Research Institute (SIPRI) was involved in the talks, though SIPRI did not return AFP's calls for a comment.
"If we can use our contacts in the best way, we will do so", she said, noting the situation on the Korean peninsula was "of interest to us all" in terms of security. Its diplomatic mission in Pyongyang, which opened in 1975, was the first Western embassy established in the country.
Ri's surprise trip to Stockholm has taken on added significance due to the expectation that a summit of Kim and Trump could defuse the tensions over North Korea's nuclear weapons program.
On Friday, Kono had a separate meeting with U.S. Deputy Secretary of State John Sullivan in Washington.
Kono and Mattis agreed that through a planned US visit by Japanese Prime Minister Shinzo Abe for talks with Trump in early April, the two allies will closely coordinate on issues related to North Korea, including a first-ever U.S.