Kim, in his New Year message broadcast on state TV, described the purge of a "faction" within the ruling party as a "resolute action", in his first public remarks about Jang since his shock execution on December 12.
"Our party took a resolute action to remove... scum elements within the party last year," Kim said, repeating the party's earlier accusation against Jang that he tried to build his own powerbase.
"Our party's timely, accurate decision to purge the anti- party, anti-revolutionary elements helped greatly cement unity of the party and the revolution and strengthened our solidarity by 100 times," he said.
Yang Moo-Jin, a professor at Seoul's University of North Korean Studies, said the speech underlined Kim's intention to portray himself as an unchallenged and stable leader, two years after he took the reins of power.
Jang, once the communist country's unofficial number two and Kim's political mentor, was executed on a range of charges including plotting a coup and corruption.
The 67-year-old played a key role in cementing the leadership of the inexperienced Kim, who took power after the death of his father and long-time ruler, Kim Jong-Il, in December 2011.

But Jang's growing political power and influence drew resentment from his nephew barely half of his age, analysts said.
Jang's purge also stemmed from political battles among Pyongyang officials to control the country's lucrative coal trade business once dominated by Jang, Seoul's spy chief said.
Kim Jong-Un stressed that the latest purge was proof that the ruling communist party was dedicated to serving the public.
Jang's execution -- the biggest political upheaval since Jong-Un took power -- raised questions over potential instability within the impoverished but nuclear-armed state.
Kim Jong-Un stepped up hostile rhetoric in his speech, saying that the Korean peninsula would be engulfed by "massive nuclear disaster" if war breaks out there again. He warned that the US would not be safe in the event of a conflict.
"If the war breaks out again in this land, it will bring about a massive nuclear disaster and the US will also never be safe," Kim said.
"We are faced with a dangerous situation in which a small, accidental military clash can lead to an all-out war."
Kim added he would not beg for peace and vowed to protect the North with strong self-defence measures against enemies.
The leader however took a slightly conciliatory posture towards the South, saying now was "high time" to ease tension between the two Koreas.


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