There is speculation that the foreign minister's visit is to lay the groundwork for Trump-Kim talks in the country, or that Sweden is helping set up the summit elsewhere.
This is the first time Abe and Moon have talked directly since North Korean leader Kim Jong Un asked to meet US President Donald Trump.
The North Korean diplomat arrived in Sweden on Thursday and held discussions with both Wallstrom and the Swedish Prime Minister Stefan Lofven. Its diplomatic mission in Pyongyang, which opened in 1975, was the first Western embassy established in the country.
No public statement from Ri or Wallstrom was expected after the conclusion of the talks on March 16 evening, but the foreign ministry said it would publish a statement.
'We've made a decision to narrow down the agenda topics to denuclearising the Korean peninsula, securing permanent peace to ease military tension and new, bold ways to take inter-Korean relations forward, said Im, who is head of the preparation team.
In the past, that has meant Washington would have to withdraw all of its troops from South Korea, a condition no USA president has been willing to consider.
Im Jong-seok, the Chief Presidential Secretary for President of South Korea Moon Jae-in, greets Kim Yo Jong, the sister of North Korea's leader Kim Jong Un, during a banquet at a hotel in Seoul, South Korea, February 11, 2018.
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"We can't rule out the possibility of a contact between the North and the US" during Ri's trip to Sweden, a Beijing source told the news agency. "But we are not naive in believing we can solve the world's problems".
Senior South Korean officials who traveled to the North Korean capital of Pyongyang this month and met with Kim say he is willing to discuss the North's nuclear weapons program. Sweden is now a non-permanent member of the Security Council.
Tokyo's insistence on including discussion on the abductions by North Korean agents could cause friction between Japan, South Korea and the USA if Seoul or Washington were willing to cut a denuclearisation deal with Pyongyang separate from any abduction pact.
"We have always said we want to be a mediator that facilitates this process", he said Friday.
Japan said on Friday that Moon had promised to help Abe resolve the issue of Japanese abducted by North Korea and agreed to keep maximum pressure on Pyongyang over its nuclear and missile programmes.
Moon also spoke with Trump on the phone on Friday, Yonhap reported.