The meeting at a North Korea-controlled building in the border village of Panmunjom comes as the international community waits to see if North Korea will begin abandoning its nuclear weapons, something officials suggested would happen after Kim's summit with President Donald Trump in June in Singapore.
North Korea is thought to have a growing arsenal of nuclear bombs and long-range missiles and to be closing in on the ability to reliably target anywhere on the US mainland.
A string of North Korean weapons tests last year, during which Pyongyang claimed to have completed its nuclear arsenal, had many in Asia worried that Washington and Pyongyang were on the brink of war.
The South Korean delegation for Monday's talks was led by Cho Myoung-gyon, who oversees Seoul's Unification Ministry, which handles inter-Korean issues, and includes Nam Gwan-pyo, a Moon aide responsible for North Korean nuclear matters.
North Korea, which proposed Monday's talks last week, also sent officials overseeing past inter-Korean economic collaborations.
Experts are seeing slow progress on efforts to disarm North Korea since the Singapore summit.
Pyongyang has urged Washington to reciprocate its goodwill gestures, which include suspending missile and nuclear tests and returning the remains of Americans who fought in the Korean War.
Washington, which cancelled an annual joint military exercise with South Korea that had taken place in August in previous years, has refused to ease sanctions until North Korea finally and fully denuclearises.
- AP