The call comes at a time of heightened tension on the Korean Peninsula following the execution of Kim's uncle and former mentor in an unusually public purge.
Kim visited the Command of Large Combined Unit 526 on Christmas Eve, the North's official Korean Central News Agency said.
"He instructed the unit to put utmost spurs on rounding off its combat readiness... always bearing in mind that a war breaks out without any prior notice," it said.
The unit is based in the North's western port city of Nampo, according to the South's Yonhap news agency.
There are growing concerns over the regime's stability after the execution of Jang Song-Thaek, a senior leader who was also the uncle and former political mentor of the younger leader.
Seoul and Washington have warned of possible provocative acts by the nuclear-armed North following the purge.
South Korean President Park Geun-Hye called for "watertight security readiness" during her trip Tuesday to a frontline guard post, describing the situation over the border as "ominous".
"We should react sternly and mercilessly to any provocations by North Korea," she said.
In recent days the reclusive state's propaganda mill has gone into overdrive describing Jang as a traitor while extolling Kim's leadership.
Tens of thousands of troops pledged loyalty to him in a mass rally on the death anniversary of his father last Tuesday.
The Kim dynasty has ruled the impoverished but nuclear-armed state since 1948 with an iron fist and pervasive personality cult.
