While reiterating his intention to meet with the North Korean leader by the end of May, Trump agreed that not words but concrete actions will be the key to achieving permanent denuclearization of the peninsula.
Kim is reportedly committed to denuclearization, but doubts persist as to whether he is serious about giving up the North's nuclear weapons.
Earlier Thursday, Ri flew into Stockholm via Beijing International airport with a team including Choe Kang-il, deputy director general for North American affairs at North Korea's Foreign Ministry.
"They had a meeting".
KBS World Radio in South Korea cited speculation the two would exchange information about the forthcoming meeting between Trump and Kim.
Swedish public broadcaster SVT reported, without citing sources, that Ri planned to stay in Sweden until Sunday.
After months of tension and warmongering over Pyongyang's nuclear programme, Trump has agreed to a summit proposal relayed by South Korean envoys who met Kim Jong-un in Pyongyang. -North Korea summit would be a good confidence-building measure. Lofven pointed out that Sweden is not militarily aligned and has had a long-standing presence in North Korea, but added that the main players had to "decide which role Sweden will play".
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Kang and Sullivan "agreed that worldwide pressure on North Korea must be maintained until the regime takes credible, verifiable and concrete steps toward denuclearization", Nauert added.
Sweden is an obvious choice for the historic summit meeting between Donald Trump and Kim Jong-un.
"We can't rule out the possibility of a contact between the North and the US" during Ri's visit, a Beijing source told South Korea's Yonhap agency. "We've been working with North Korea".
"We'll see what happens next", Wallstrom said. In 1975 Sweden opened its diplomatic mission in Pyongyang. The villa is close to the embassies of South Korea and the United States.
In the US, the South Korean minister also had plans to meet House Speaker Paul Ryan.
Im Jong-seok, chief of staff for South Korean President Moon Jae-in, told a press briefing that the Moon government will push for a senior-level dialogue with the DPRK in late March for the inter-Korean summit agreed to be held in late April.