Foreign Minister Margot Wallstrom told Swedish news agency TT that experts in nuclear disarmament, economic development and regional security attended the diplomats' meeting in Sweden.
The first meeting ever to bring the leaders of North Korea and the United States face-to-face took place in June when Kim and Trump met in Singapore.
Trump said Saturday he is aiming to have a second summit in late February with the goal of producing a deal attractive enough to persuade Kim to give up North Korea's nuclear weapons.
Lee Do-hoon of South Korea and Steve Biegun, U.S. special envoy for North Korea negotiations, planned to attend "small format" talks with North Korean Deputy Foreign Minister Choe Son Hui, the Swedish Foreign Ministry said Sunday
The Swedish government and the Stockholm International Peace Research Institute, an independent think-thank focused on research on conflicts, armaments and arms control, were co-hosting the talks.
Wallstrom didn't disclose the venue or schedule for the talks. Swedish media said they were thought to be underway at Hackholmssund, a conference center northwest of Stockholm on Lake Malaren.
Sweden has had diplomatic relations with North Korea since 1973 and is one of only a few Western countries with an embassy there. It provides consular services for the United States.
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