Kim said this at a meeting with high-ranking Workers Party officials days after Pyongyang successfully tested its most advanced intercontinental ballistic missile (ICBM) to date, Efe quoted the KCNA report.
Kim's speech came on the same day the UN Security Council planned to vote on a new proposal from the US to expand sanctions against the isolated Asian country, in response to the ICBM test conducted on November 29.
According to the North Korean regime, it was now capable of carrying a large nuclear warhead and reaching all US territory.
"The rapid development of North Korea's nuclear force is now exerting big influence on the world political structure and strategic environment," Kim said in his opening address.
"Nobody can deny the entity of North Korea which rapidly emerged as a strategic state capable of posing a substantial nuclear threat to the US," Kim said.
The leader also stressed that Pyongyang was facing "grave challenges that should not be overlooked", although he called on the North Korean people to be "optimistic about progress of our revolution under this situation" instead of feeling "disappointed" by or "afraid" of such challenges.
The US-drafted resolution were aimed at further cutting Pyongyang's access to hydrocarbons and order the repatriation of North Koreans working outside the country, according to diplomatic sources.