South Korean President Park Geun-Hye warned Monday that North Korea's recent submarine-launched ballistic missile test posed a "serious challenge" to regional stability and vowed a strong military response to any provocation from Pyongyang.

Pyongyang's state media announced Saturday that a new SLBM had been successfully tested under the personal supervision of North Korean leader Kim Jong-Un, who described it as a "world-level strategic weapon".

The test rang alarm bells in Seoul because a fully developed SLBM capability would take the North Korean nuclear threat to a new level, allowing deployment far beyond the Korean peninsula and the potential to retaliate in the event of a nuclear attack.

Pyongyang's development of an SLBM "is a serious challenge to stability on the Korean peninsula and in Northeast Asia," Park told a specially-convened meeting of senior ministers and security advisers.

South Korean troops will retaliate "sternly" in the event of any provocation by North Korea, especially near the disputed Yellow Sea border, a statement from the presidential Blue House quoted her as saying.

The North Korean test was widely believed to have been an ejection test -- with the missile only travelling a few hundred metres -- rather than a full flight test, and South Korea's initial assessment was that the North was still in the "early phase" of development.

But an unnamed defence official later said the North could have a functioning submarine armed with ballistic missiles in two to three years, with operational field deployment one or two years after that.

The North followed up the SLBM launch by test firing three anti-ship cruise missiles on Saturday.

Pyongyang has threatened to fire on sight at South Korean navy patrol boats it accuses of routinely entering its territorial waters in the Yellow Sea.

Seoul has denied any incursions.