Speaking at a Korean War anniversary event, Mr Kim added that the country was “fully ready for any military confrontation” with the US, state news agency KCNA reported.
The comments come amid concern that North Korea could be preparing a seventh nuclear test.
The US warned last month that Pyongyang could conduct such a test at any time.
North Korea’s most recent nuclear test was in 2017. However, tensions have been rising on the Korean peninsula.
The US special representative to North Korea Sung Kim says North Korea has tested an unprecedented number of missiles this year – 31 compared to 25 during the whole of its last record-breaking year, 2019.
In June South Korea responded by launching eight missiles of its own.
Although the 1950-53 Korean War ended in a truce, North Korea claims it as a victory against the US. The annual “Victory Day” celebrations are marked by military parades, fireworks and dancing.
In his speech to mark the event, Mr Kim said nuclear threats from the US required North Korea to achieve the “urgent historical task” of beefing up its self-defence.
The US had misrepresented North Korea’s regular military exercises as provocations, he added.
Mr Kim also appeared to address reports that South Korea is moving to revive a plan to counter the North Korean nuclear threat by mounting precautionary strikes in the event of an imminent attack.
The so-called “Kill Chain” strategy, first elaborated a decade ago, calls for pre-emptive strikes against Pyongyang’s missiles and possibly its senior leadership.
Some analysts have warned it carries its own risks and could fuel an arms race.
At the Victory Day celebration Mr Kim said that South Korean president Yoon Suk-yeol’s government and military would be “obliterated” if he carried out pre-emptive strikes.