He told military leaders North Korea would revise its military posture to be ready to launch pre-emptive strikes, the Korean Central News Agency said.
On Wednesday the UN imposed some of its toughest ever sanctions on North Korea, following its recent nuclear test and missile launch.
In response, the North fired six short-range projectiles into the sea.
KCNA said Mr Kim was speaking at a military exercise on Thursday, which is thought to be when the projectiles were fired.
He said North Korea “must always be ready to fire our nuclear warheads at any time” because enemies were threatening the North’s survival.
“At an extreme time when the Americans… are urging war and disaster on other countries and people, the only way to defend our sovereignty and right to live is to bolster our nuclear capability,” he was quoted as saying.
Such rhetoric is not unusual from North Korea, but despite its recent nuclear and ballistic tests, analysts still doubt it has the ability to make a nuclear bomb small enough to put on a feasible missile. READ MORE OF THIS STORY