Mr Kim is said to have personally supervised the test of the ballistic missiles.
"We have the sure capability to attack in an overall and practical way the Americans in the Pacific operation theatre," he was quoted by the North Korean state news agency as saying.
Outside experts do not believe, though, that North Korea has the ability to build nuclear warheads small enough to put on its missiles, though it is continually striving to get them, Korea correspondent Steve Evans reports.
It is also testing missiles fired from submarines. A functioning nuclear arsenal is probably some years away though progress towards it is steady, our correspondent adds.