In front of cheering crowds, the new leader praised and offered respect to Kim Il-Sung – his grandfather – and his father, the late Kim Jong-Il.
As part of the celebrations, a huge military parade has been staged in the main square of Pyongyang.
Kim Jong-Un’s speech comes just two days after a failed rocket launch.
The attempted launch was condemned by the international community, amid concern that it was a covert test of long-range missile technology.
On Sunday, television footage showed thousands of soldiers carrying red flags marching into the square to the sound of drumbeats.
It is the first time Kim Jong-Un, believed to be in his late 20s, has been seen speaking publicly since taking power following the death of his father in December.
“I express my greetings to our compatriots in South Korea and across the world who dedicate themselves to reunification and the prosperity of the nations,” Kim Jong-Un said reading from a script, in an address which lasted more than 20 minutes, as the crowds applauded throughout.
“Let us move forward to final victory.”
Kim Jong-Un praised the country’s “military first” policy.
“Superiority in military technology is no longer monopolized by imperialists,” he said.
After the speech, soldiers marched past and saluted the leader. They were followed by tanks and artillery, and then an array of truck-mounted missiles.
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