Ri was travelling with Choe Kang Il, deputy director general of the foreign ministry's North America section, according to South Korea's Yonhap news agency.
After South Korea's high-ranking delegation visit to North Korea on March 5-6, Kim expressed his willingness to hold talks with the U.S. president.
It added that a statement summarizing the talks will be made available Friday after Ri's talks with Foreign Minister Margot Wallstrom.
During a joint press conference at the White House on March 6, Swedish Prime Minister Stefan Löfven offered his country's help in facilitating talks between the USA and North Korea, highlighting his country's 45-year diplomatic presence in Pyongyang.
The committee also chose to push for performances in Pyongyang by South Korea's art troupe and taekwondo demonstration team early next month as was agreed between the South Korean presidential envoys and North Korean leader Kim Jong-un early last week.
Earlier on Friday, Ri also met Swedish Prime Minister Stefan Lofven, the latter's press secretary, Erik Nises, toldCNN.
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.
North Korean foreign minister Ri Yong Ho is on his way to Sweden for a two-day trip, the Swedish Ministry for Foreign Affairs announced on Thursday.
In talks that started Thursday and are expected to continue on Friday, the North Korean and Swedish delegations will discuss several topics, including the security situation on the Korean Peninsula, a spokesperson for the Swedish Foreign Ministry said. Its diplomatic mission in Pyongyang, which opened in 1975, was the first Western embassy established in the country.
Wallstrom earlier said Sweden hopes "we can use our role and also our contacts" to facilitate U.S. "The aim of the visit is to contribute to the effective implementation of the resolutions" voted by the Security Council against Pyongyang over its nuclear programme, as well as those calling "for intensified diplomatic efforts to find a peaceful solution to the conflict".
North Korea admitted in 2002 it had kidnapped 13 Japanese in the 1970s and 1980s to train spies, and five of them returned to Japan.
But diplomatic sources have signaled enough confidence in South Korea's words and actions that most of the parties are pressing ahead.
The offer for a meeting comes after months of escalating rhetoric between Trump and Kim over North Korea's repeated missile and nuclear tests.
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