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The address by Kim, who took over power in the reclusive state after his father, Kim Jong-il, died in 2011, appeared to take the place of the policy-setting New Year editorial published in leading state newspapers.
Impoverished North Korea raised tensions in the region by launching a long-range rocket in December that it said was aimed at putting a scientific satellite in orbit, drawing international condemnation.
North Korea, which considers North and South as one country, the Democratic People's Republic of Korea, is banned from testing missile or nuclear technology under U.N. sanctions imposed after its 2006 and 2009 nuclear weapons tests.
"An important issue in putting an end to the division of the country and achieving its reunification is to remove confrontation between the north and the south," Kim said in the address that appeared to be pre-recorded and was made at an undisclosed location.
"The past records of inter-Korean relations show that confrontation between fellow countrymen leads to nothing but war."
The New Year address was the first in 19 years by a North Korean leader after the death of Kim Il-sung, Kim Jong-un's grandfather. Kim Jong-il rarely spoke in public and disclosed his national policy agenda in editorials in state newspapers.
The two Koreas have seen tensions rise to the highest level in decades after the North bombed a Southern island in 2010 killing two civilians and two soldiers.
The sinking of a South Korean navy ship earlier that year was blamed on the North but Pyongyang has denied it and accused Seoul of waging a smear campaign against its leadership.
Last month, South Korea elected as president Park Geun-hye, a conservative daughter of assassinated military ruler Park Chung-hee whom Kim Il-sung had tried to kill at the height of their Cold War confrontation.
Park has vowed to pursue engagement with the North and called for dialogue to build confidence but has demanded that Pyongyang abandon its nuclear weapons ambitions, something it is unlikely to do.
Conspicuously absent from Kim's speech was any mention of the nuclear arms programme.