The Swedish Foreign Ministry said on Friday night that Ri and Wallstrom planned to meet again Saturday and a summary of their discussions would be provided afterward.
The two ministers are likely to discuss issues such as North Korea's ongoing detention of three U.S. citizens ahead of the upcoming summit between U.S. President Donald Trump and North Korean leader Kim Jong Un.
"Now that the preparatory committee has been formed, we can make a meeting proposal first or if the North is prepared, it may do so first", the official said.
"We are hoping that if we can use our role and also our contacts, then we will put them to the best use", Wallstrom told reporters.
The country has had diplomatic relations with Pyongyang since 1973 and provides support for American interests there. North Korea and the U.S. are considered unlikely.More news: Syrian President Assad visits army positions in eastern Ghouta - state media
As to foreign media reports that a meeting between U.S. President Donald Trump and the North's leader, which is expected to take place by May, could be pushed back to June or July, the official said that the U.S. hasn't notified the South of anything yet.
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.
Swedish Foreign Minister Margot Wallström said Friday that the country is ready to host talks between North Korea and the USA, saying the Swedish government "values this opportunity to arrange a meeting".
Global media have speculated that Sweden could be a potential location if the summit were to be confirmed.
Some media have reported that Ri, who was stationed at North Korea's embassy in Stockholm from 1985 to 1988, will stay in the Scandinavian country until tomorrow, though Swedish officials would not confirm this.More news: Ireland beat arch-enemy England to complete Grand Slam
"We have always said we want to be a mediator that facilitates this process", Lofven said.
Meanwhile, Japanese broadcaster TBS said Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in discussed North Korea in a telephone call on Friday.
TBS said Abe told Moon he wanted North Korea to not only suspend nuclear and missile testing, but also accept International Atomic Energy Inspectors on its soil.
The ministry said the talks will also focus on those consular responsibilities.
"We are a country that is militarily non-aligned and have a longstanding presence in North Korea, and with the trust we enjoy we think we can play a role". Trump accepted the invitation to meet with Kim by the end of May.More news: Raiders trading Cordarrelle Patterson to the Patriots
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