The train, which departed Pyongyang around 5 p.m. local time, is expected to pass China en route Vietnam, according to the Russian news agency. The journey would span approximately 4,500 kilometers and last for over two days.
The first summit between the two leaders was held in Singapore in June 2018, but negotiations failed to make much headway owing to disagreements over the concept of denuclearization.
Kim Jong-un will also pay an official visit to Vietnam in the coming days at the invitation of Party General Secretary and State President Nguyen Phu Trong.
A statement by Vietnam's Ministry of Foreign Affairs on Saturday did not mention specific dates for the visit, which will be Kim's first to Vietnam.
Kim boarded a Boeing 747 from Air China to Singapore for the first summit last year. But when he visited China the same year, he used his own specialized steel-plated train instead.