Kim watched the test of the "highly intelligent" rockets to be deployed at naval units, Pyongyang's KCNA news agency reported Monday.
He "noted with great pleasure that it marked another fresh milestone in bolstering up the Juche (self-reliance)-based naval force," it said.
"Ultra-modern strike means of Korean style have been studied and developed one after another recently to completely contain the hostile forces," Kim was quoted as saying.
The South's defense ministry said the North had tested three short-range missiles with a range of nearly 100 kilometers (62 miles) Sunday off its east coast.
"North Korea appears to be developing new missiles that would replace its old Soviet-designed anti-ship missiles," ministry spokesman Kim Min-Seok told reporters.
The test was the latest since Pyongyang claimed on May 9 it had successfully test-fired an SLBM - a technology that could eventually offer the nuclear-armed state a survivable second-strike capability.
A fully developed SLBM capability would take the North Korean nuclear threat to a new level, allowing deployment far beyond the Korean peninsula.
But some experts have questioned the authenticity of the May test, saying photos of the launch might have been digitally manipulated.
North Korean leader Kim Jong-un has watched a test-firing drill of a new type of anti-ship rockets, which is being deployed at the military's naval units, the North's media said Monday.