The remarks come a day after KCNA said North Korea's national assembly amended the constitution to designate South Korea a "hostile state", in line with Kim's vow to drop unification of the two Koreas as a national goal.
Kim also said the changed nature of the South Korea/US alliance, and their different, more developed military manoeuvres highlight the importance of a stronger North Korean nuclear deterrent.
As for North Korea's military blasting road and rail links with South Korea this week, Kim said it means "not only the physical closure but also the end of the evil relationship with Seoul" as well as "the complete removal of the useless awareness about fellow countrymen and unreasonable idea of reunification."
Pyongyang had said last week it would cut off inter-Korean paths entirely and further fortify the areas on its side of the border as part of its push for a "two-state" system scrapping its longstanding goal of unification.
Kim made the remarks while inspecting the headquarters of the 2nd Corps of North Korean army on Thursday, KCNA said.
In January, Kim called for a constitutional amendment to erase unification as a goal in its ties with the South, accusing Seoul of colluding with the United States to seek the collapse of his communist regime and a clear defining of its territory.
North Korea's Supreme People's Assembly met over two days last week where it had been expected to amend the constitution to officially designate South Korea as a separate country and a main enemy.
South Korea said its policy was to continue to pursue national unification but respond with force if North Korea mounts any aggression.
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