The meetings between the foreign ministers of the two countries in Sweden came a week after Trump agreed to a summit proposal relayed by South Korean envoys who met Kim in Pyongyang.
Few details are available, but the meeting was confirmed to CNN by the Finnish and South Korean foreign ministries, and the South Korean news agency Yonhap reported that the North Korean official responsible for United States affairs was spotted at the Beijing airport heading to Finland.
Choe Kang Il, North Korea's Deputy Director-General for North American Affairs at the foreign ministry, was spotted at Beijing Capital International Airport on Sunday as he boarded a morning plane to Helsinki, No Cut News reported. Since the announcement, North Korea has fallen silent, raising questions about the summit's certainty.
Koizumi was the first Japanese prime minister to visit North Korea.
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"We agreed on the need to resolve the abduction issue", Kono told journalists after the talks.
"The foreign ministers discussed opportunities and challenges for continued diplomatic efforts to reach a peaceful solution to the conflict as well as bilateral relations", the Swedish Foreign Ministry said in a statement.
Sweden's Foreign Minister Margot Wallstrom comments on a meeting with North Korean Foreign Minister Ri Yong Ho, in the Swedish house of parliament in Stockholm, March 16, 2018.
In a phone call with South Korean President Moon Jae-in, Trump expressed "cautious optimism" over recent developments regarding North Korea. And he has been in close touch with the director of South Korea's National Intelligence Service, Suh Hoon, who American officials said brokered Mr. Kim's invitation to Mr. Trump.
During the visit, Moon will attend a summit with his Vietnamese counterpart Tran Dai Quang, and meet other government leaders, including General Secretary of the Communist Party Nguyen Phu Trong.
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The South Korean president's economic delegation will include top executives of Samsung Electronics, the Hyundai Motor Group, SK Innovation and LG Chem, Yonhap reported.
Choe, experienced in negotiations with the US, is expected to meet the retired American diplomat as well as other retired South Korean diplomats, the South's Yonhap news agency said, citing an unnamed diplomatic source.
Ojea Quintana also prodded Pyongyang to promptly investigate "unresolved cases of abductions involving citizens of Japan, the Republic of Korea and other states", referring to South Korea by its formal name.
In his first State of the Union address in January, Trump condemned "the cruel dictatorship" in Pyongyang over its human rights record, including its treatment of Otto Warmbier, a University of Virginia student who died a year ago soon after his release from North Korea in a coma following more than 17 months' imprisonment.
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