The North Korean leader's comments come as the UN met to discuss Tuesday's test of a ballistic missile designed to carry a nuclear payload over Japan.
Pyongyang's official Korean Central News Agency said it was a Hwasong-12 intermediate range missile that the North first successfully tested in May and threatened to fire into waters near Guam earlier this month.
Mr Kim was present for intermediate range missile launch over Japan.
He expressed "great satisfaction" over the launch which he called a "meaningful prelude" to containing Guam, which is home to key US military bases that North Korea finds threatening.
He said it is "necessary to positively push forward the work for putting the strategic force on a modern basis by conducting more ballistic rocket launching drills with the Pacific as a target in the future".
Following the launch US President Donald Trump said "all options are on the table".
"The world has received North Korea's latest message loud and clear: this regime has signalled its contempt for its neighbours, for all members of the United Nations, and for minimum standards of acceptable international behaviour.
"Threatening and destabilising actions only increase the North Korean regime's isolation in the region and among all nations of the world."
The UN Security Council strongly condemned North Korea's launch, calling its actions "outrageous" after an emergency meeting on the missile test.
"The Security Council, resolute in its commitment to a denuclearised Korean Peninsula, emphasises the vital importance of immediate, concrete actions by the DPRK to reduce tensions in the Korean Peninsula and beyond," the council said.
The council also said it was committed to a peaceful, diplomatic and political solution to the situation.
China and Russia's ambassadors to the UN said they opposed any unilateral sanctions on North Korea and reiterated calls to halt deployment of a US missile defence system in South Korea.
