Kim warned the US should not misjudge the reality that its mainland is in the North's "sighting range for strike," the North's official KCNA news agency reported.
The North fired a ballistic missile that landed in the sea near Russia on Sunday in a launch that Washington called a message to South Korea; days after its new president took office pledging to engage Pyongyang in dialogue, AFP reported.
The missile was launched at the highest angle so as not to affect the security of neighboring countries and flew 787 kilometers reaching an altitude of 2,111.5 kilometers, KCNA said.
"The test-fire aimed at verifying the tactical and technological specifications of the newly developed ballistic rocket capable of carrying a large-size heavy nuclear warhead," KCNA said.
North Korea is believed to be developing an intercontinental ballistic missile (ICBM) capable of carrying a nuclear warhead and reaching the US mainland.
The US military's Pacific Command said the type of missile that was fired was "not consistent with an intercontinental ballistic missile".
The UN Security Council is due to meet on Tuesday to discuss North Korea's latest missile launch, diplomats said, which was requested by the US and allies South Korea and Japan.