In a speech on North Korea's founding anniversary on Monday, Kim said the country must more thoroughly prepare its "nuclear capability and its readiness to use it properly at any given time in ensuring the security rights of the state", said KCNA.
A strong military presence is needed to face "the various threats posed by the United States and its followers," he added.
Kim also said North Korea is facing a "grave threat" from what it said was a US-led nuclear-based military bloc in the region.
South Korea will hold a defence ministerial meeting with the member states of the United Nations Command (UNC) on Tuesday.
The UNC is led by the commander of the U.S. military stationed in South Korea.
Last month, Germany became the latest to join the UNC in South Korea that helps police the heavily fortified border with North Korea and has committed to defend the South in the event of a war.
North Korea has criticised the UNC as an "illegal war organisation" and Germany's entry into the US-led U.N. border monitoring force as raising tensions.