The US, joined by Britain, said yesterday's apparent test was a violation of UN Security Council resolutions and called on the North to refrain from further moves that could destabilise the region.
South Korea's defence ministry said the launch appeared to have failed as the missile, fired from a submarine in the Sea of Japan, flew just 30 kilometres.
However the North's state-run KCNA news agency insisted that the test, which it said was personally monitored by Kim, confirmed "the reliability of the Korean-style underwater launching system".
"This eye-opening success constitutes one more precious gift the defence scientists and technicians are presenting to the great leaders and the party," it added.
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North Korea has been pushing to acquire submarine- launched ballistic missile (SLBM) capability that would take its nuclear strike threat to a new level, allowing deployment far beyond the Korean peninsula and the potential to retaliate in the event of a nuclear attack.
The isolated country has conducted a number of what it says were successful SLBM tests, but experts question the claim, suggesting Pyongyang had gone little further than a "pop-up" test from a submerged platform.
Tension has been running high on the divided Korean peninsula since Pyongyang's fourth nuclear test in January and rocket launch a month later widely seen as a disguised ballistic missile test.
The UN Security Council responded by slapping its strongest sanctions to date last month.
Pyongyang has since staged a series of short- and mid- range missile tests, claiming it had acquired significant technical breakthroughs in its nuclear strike capability.