The three-year Korean War ended 71 years ago on July 27, 1953 with a ceasefire that has never been replaced by a peace treaty.
Pyongyang regards the conflict as a victory, and the anniversary is a public holiday.
Kim said on Friday that it was the "sacred mission and duty of our generation" to "reliably defend our ideology and social system" and "build a people's paradise", according to Pyongyang's Korean Central News Agency.
The North Korean leader also hailed China's support during the war and said the "friendship established as the ties of kindred would be firmly carried forward".
He visited memorials honouring the veterans of the war, including the Tower of Friendship commemorating the Chinese People's Liberation Army soldiers who fought alongside North Korean forces, KCNA said.
Pyongyang's state media also said young North Koreans celebrated the anniversary, vowing to "to inherit the soul of the victorious wartime generation".
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