"If North Korea carries out a military provocation on our territory and people again, we must retaliate immediately and strongly until they completely surrender," Kim said in a speech Saturday to senior military officials.
Kim's predecessor resigned after the South was criticized for not reacting strong enough following the North's attack on the South Korean island of Yeonpyeong. Four people, two South Korean marines and two civilians, were killed in that Nov. 23 attack.
Meantime, the U.S. and Japan have started their annual military exercises off the Korean peninsula in the Pacific Ocean.
The drill involves tens of thousands of troops from both sides and the USS George Washington carrier and its battle group.
The Associated Press Contributed to this report.