The comments, carried by the North's official KCNA news agency, marked a further escalation of tension on the Korean peninsula after the UN Security Council on Wednesday imposed harsh new sanctions against the isolated state for its nuclear programme.
Kim made the comments as he supervised military exercises involving newly developed rocket launchers, KCNA reported. It did not mention the date of the drills but said the new weapons had South Korea within range.
South Korea's defence ministry said on Thursday North Korea launched several projectiles off its coast into the sea up to 150km away, an apparent response to the UN sanctions.
Kim said North Korea should "bolster up (its) nuclear force both in quality and quantity" and stressed "the need to get the nuclear warheads deployed for national defence always on standby so as to be fired any moment," KCNA quoted him as saying.
"Now is the time for us to convert our mode of military counteraction toward the enemies into an preemptive attack one in every aspect."
North Korea has previously threatened pre-emptive attacks on its enemies including South Korea, Japan and the United States.
Military experts doubt it has yet developed the capability to fire a long-range missile with a miniaturised warhead to deliver a nuclear weapon as far as the United States.
"We urge North Korea to refrain from provocative actions that aggravate tensions and instead focus on fulfilling its international obligations and commitments," said Commander Bill Urban, a US Defense Department spokesman, responding to the report.
Possible engine test eyed
A US-based think tank said recent commercial satellite imagery showed new activity at North Korea's Sohae Satellite Launching Station that could be preparations for a rocket-engine test.
Johns Hopkins University's 38 North project, which monitors North Korea, said an image from Feb 21 showed an unusual convoy of trucks near the vertical engine test stand.
"One possibility is that these vehicles are returning from a delivery of supplies, fuel, or even engine components for testing to the stand," the report said.
North Korea had taken steps at Sohae in past months to better conceal preparations for space launches and engine tests, making identifying preparations for launches using commercial satellite images more difficult, 38 North said.
South Korean President Park Geun-hye on Thursday repeated a stern warning against the North to abandon its nuclear ambitions and said should would work to "end tyranny" by the North's leader.
Last month, Seoul suspended the operation of a jointly run factory project with North Korea that had been the rivals' last remaining venue for regular interaction.
