The weapons tests come as the US and South Korea last week launched annual major drills in South Korea.
Kim said the drill would expose "the enemies within the 420-km striking range, to uneasiness" and "give them a deep understanding of the destructive power of tactical nuclear weapons.
Images from state news agency KCNA showed Kim and his daughter and potential successor, known as Kim Ju-ae, were watching the weapons tests, on Saturday, local time.
"The launched rockets battered the island target in the East Sea of Korea about 364.4 km away with the accuracy of 100 per cent," KCNA said.
South Korea's military said North Korea fired more than 10 ballistic missiles towards the sea off the nation's east coast.
The missiles were launched from an area near the capital Pyongyang about 1.20pm local time and flew about 350km, Seoul said.
Last week, North Korea's Kim Yo-jong, Kim Jong-un's sister, said US-South Korea military drills were a "provocative and aggressive war rehearsal" that would harm regional stability.
South Korea and Washington say the drills are purely defensive and aimed at testing readiness against military threats from North Korea.
On Sunday, North Korea said it would frequently conduct such regular drills for checking the DPRK's war deterrence.
North Korea has test-launched a wide range of ballistic and cruise missiles for more than two decades in a push to develop the means to deliver nuclear weapons, which it is believed to have successfully built.
As a result, Pyongyang has been under multiple UN Security Council sanctions since 2006 but it remains defiant, despite severe obstacles they created to its trade, economy and defence.
On Thursday, South Korea's Prime Minister Kim Min-seok met US President Donald Trump in Washington to discuss ways to reopen dialogue with the North.
Trump is eager for any opportunity to sit down with North Korea's Kim Jong-un, South Korea's Kim told reporters.
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