A photo of the leader of the isolated state showed a smiling and wind-swept Kim standing on a snow-covered mountaintop, the sun rising behind him.
"Climbing Mt. Paektu provides precious mental pabulum more powerful than any kind of nuclear weapon," the Rodong newspaper quoted Kim as saying.
The story is the latest run by state media on the feats of the Kim dynasty, which has ruled for more than six decades with an iron fist and pervasive personality cult.
The 2,750-metre peak of the volcanic mountain, lying on the border with China, is considered a sacred place in Korean folklore and plays a central role in the propaganda glorifying the Kim family.
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Pyongyang's state hagiography has it that Kim Jong-Il was born on the mountain -- although many historians say he was born in Russia -- and praises the family for their "Mt. Paektu bloodline".
Kim, like his predecessors, has made frequent "field guidance trips" to industrial plants, army bases, and sacred sites across the country in what analysts say is an attempt at forging an image as an energetic man of the people.
Kim, who took over after the death of his father in 2011, seeks seemingly impossible policy goals of improving the economy and developing the atomic arsenal simultaneously.