The US mainland and the Pacific are now "within the striking range" of the North's army, the official KCNA news agency reported Kim as saying after Wednesday's launch.
The missile was fired from a submarine submerged off the northeastern port of Sinpo on Wednesday, according to South Korea's military. It flew 500 kilometres towards Japan, far exceeding any previous sub-launched tests.
The UN Security Council met for two hours yesterday to discuss North Korea's latest provocative move and agreed to consider a statement condemning the launch.
However diplomats expected further haggling with China, Pyongyang's main ally, over the wording.
Earlier this month, North Korea fired a land-launched ballistic missile directly into Japanese-controlled waters for the first time, drawing an outraged response from Tokyo.
But the Security Council failed to condemn the move after China sought to include language in a statement opposing the THAAD missile defence system that the United States plans to deploy in South Korea.
Pyongyang's top newspaper Rodong Sinmun carried 24 photos of him observing the launch, including one with his hands on his hips roaring with laughter at an observation post, and other watching through a pair of binoculars.
"He appreciated the test-fire as the greatest success and victory," it said.
Kim called for his nation's scientists to work towards mounting nuclear warheads on all types of ballistic missiles and to be able to deliver them in order "to cope with the unpredicted total war and nuclear war with the US imperialists."
A proven submarine-launched ballistic missile (SLBM) system would take its nuclear strike threat to a new level, allowing deployment far beyond the Korean peninsula and a "second-strike" capability in the event of an attack on its military bases.
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