Kim had asked Korean Workers' Party cadres to build the new submersible by Sept. 9, 2018, the 70th anniversary of the founding of the North Korean government, the Tokyo Shimbun reported on Friday.
The mandate was issued in June 2015 and Kim allegedly told his military industry chief Ri Man Gon that if he succeeds, he would "raise a statue" in Ri's honor, according to the report.
Only one missile can be mounted on the 2,000-ton Sinpo-class submarine believed to have been used for the SLBM launch on Wednesday. Launches also can take place only at a depth of 10 meters below the water's surface with the current technology.
North Korea is concurrently planning the development of a 3,000-ton submarine capable of carrying three submarine-launched ballistic missiles, Japan's Nihon Keizai reported on Friday.
While North Korea touted the Wednesday SLBM launch as a victory on Thursday, Pyongyang has yet to achieve final-phase induction, meaning the technology has not been perfected.
Kim has been very attentive to the SLBM development program, and visited the development site more than 10 times prior to launch according to Pyongyang's KCNA and Rodong Sinmun.
KCNA has stated Kim "has a direct tight grasp on the construction of powerful strategic submarines and ballistic missiles, owing to the dedication of his labor and heart to the tenacious push" for their development.
Kim Keun-sik, a professor of political diplomacy at South Korea's Kyungnam University told JoongAng Ilbo the SLBM could be the "trademark" of the Kim Jong Un period of rule, since development did not begin until after he assumed power.
According to Japan's Defense White Paper North Korea retains 78 submarines and other submersibles, including the 3,500-ton Golf-class submarine that Russia sold to North Korea for scrap in the '90s.