In a speech marking the anniversary of North Korea's founding, Kim said the country must better prepare its "nuclear capabilities and be prepared to use them properly at any time to ensure the state's right to security."
He added that a strong military presence is needed to counter various threats from the United States and its allies.
Kim also said North Korea allegedly faces a "serious threat" from the U.S.-led nuclear military bloc in the region.
Reaction from the civilized world
South Korean Vice Defense Minister for Policy Cho Chang-rae and his U.S. and Japanese counterparts on September 10 condemned Pyongyang's recent diversification of nuclear delivery systems and the testing and launching of several ballistic missiles.
At the meeting in Seoul, the three leaders reaffirmed their commitment to strengthening trilateral cooperation to ensure peace in the region, including by containing nuclear and missile threats from North Korea.
They also agreed to hold a second trilateral military exercise, called Freedom Edge, in the near future.
South Korea will also host a defense ministers’ meeting with the United Nations Command (UNC) on September 10. The UNC is led by the commander of the US military forces stationed in South Korea.
Last month, Germany became the latest country to join the UNC in South Korea, which helps guard the heavily fortified border with North Korea and has pledged to defend the South in the event of war.
North Korea is believed to have around 20 nuclear warheads.
Seoul has previously said North Korea may conduct a nuclear test before the US presidential election.