The comments raise the stakes as each side steps up displays of military force in a standoff over the isolated country's nuclear weapons and ballistic missile programmes.
The defense minister's statement also accused the United States and South Korea of escalating tensions in the region while criticizing the first meeting by their nuclear consultative group.
"The ever-increasing visibility of the deployment of the strategic nuclear submarine and other strategic assets may fall under the conditions of the use of nuclear weapons specified in the DPRK law," the statement said.
DPRK is short for the North's official name, the Democratic People's Republic of Korea.
The remark is aimed at the Ohio-class U.S. nuclear-powered submarine which arrived at a port in the southern city of Busan earlier this week.
"The phase of a military clash on the Korean peninsula has surfaced as a dangerous reality," the KCNA report added.
The report comes after a U.S. soldier crossed the border into North Korea on Tuesday at a time of heightened tension between the two Koreas and the United States.
North Korea has yet to comment on the incident involving the U.S. soldier.
Last year, the reclusive state codified a new, expansive nuclear law declaring its status as a nuclear-armed state "irreversible."
"The utmost significance of legislating nuclear weapons policy is to draw an irretrievable line so that there can be no bargaining over our nuclear weapons," North Korea's leader Kim Jong Un was quoted as saying at that time by KCNA.
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