It has carried out numerous other missile tests, including in March when it fired four ballistic missiles into the Sea of Japan.
The North has conducted two nuclear tests and test-fired more than two dozen missiles since a year ago.
In September, North Korea announced the successful ground test of a new type of "high-power engine", apparently for launching satellites.
"We do not want to interfere in (other country's) political matters, but it is our responsibility to investigate a murder case which occurred within our jurisdiction". It said the engine met technical expectations.
Kim emphasized the whole world would "soon witness what eventful significance the great victory won today carries", KCNA reported.
North Korea has been referring to the deceased as Kim Chol, the name that appeared in the victim's passport, and has rejected the police findings that VX was used to kill him.
Kim also hailed the country's weapons industry for a "series of unprecedented successes".
Apparently satisfied with the outcome of the test, Kim is shown in the front-page photo celebrating, surrounded by cheering North Korean officials.
Malaysia's once-cosy ties with North Korea have frayed in the wake of Kim Jong Nam's assassination.
Rookie Secretary of State Rex Tillerson on Friday wrapped up his first visits to Japan and South Korea before heading to China, and in one of his strongest statements about anything to date, he warned Pyongyang that its provocative actions would not be tolerated and talked of a pre-emptive strike.
At the time, Pyongyang checked an 80 ton force rocket that burned for 200 seconds.
The rocket engine that North Korea tested appeared to be powered with liquid fuel, according to Melissa Hanham, an expert at the James Martin Center for Nonproliferation Studies, rather than the solid fuel the regime's engineers have been working on recently.
Local sources, however, said that while the rocket seemed similar, the flames coming out of it were darker and they detected three smaller side thrusts surrounding the main column of flame leaving the engine.
The DPRK's Saturday could have been the "final test" of the carrier rocket for the geostationary satellite that was observed by Kim Jong Un in September past year, Kim Dong-yup, a researcher at the Institute for Far Eastern Studies told NK News. This can make it into a viable engine for an ICBM that Pyongyang has said it will develop to target the USA mainland.
The UN believes North Korea is using its so-called space programme to design a missile capable of hitting the US.