Pyongyang said Ri Yong-ho's trip was for "bilateral relations and issues of mutual concern".
Sweden has a long history of mediating between Washington and Pyongyang.
Mr Ri had already met his Swedish counterpart Margot Wallstrom late on Thursday and early on Friday.
Sweden's foreign ministry said their discussions would focus on tensions between the two Koreas, and Sweden's diplomatic work on behalf of the US in North Korea.
Mr Ri's visit has been extended from the scheduled two days, and he will now stay in Sweden until Sunday, Sweden's SVT Nyheter reports.
The agenda of the talks has broadened, the news site says. One topic is said to be confidence-building measures with the US, including the release of US citizens from North Korean detention.
There has been no official word from North Korea since the invitation was delivered via South Korean officials in Washington.
Sweden's prime minister told his country's news agency TT that "if the main actors want Sweden to play a role then we are ready to do that".
"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. But it has to be the main actors who decide which role Sweden will play."
No sitting US president has ever met a North Korean leader.
Such a summit, which Pyongyang has long wanted, has previously been seen as possible only after major concessions from the North Koreans.
North Korea's defiant nuclear and missile programme has led to severe international sanctions against Pyongyang in the hope they would force the regime to abandon its military threats.
