Pyongyang's official Rodong Sinmun newspaper published photos that show Mr Kim, equipped with binoculars and smiling widely, observing the firing of rocket artillery and what appeared to be a short-range ballistic missile fired from a launch vehicle.
Experts say the missile was identical to the one the North launched on Saturday, which appeared to be a solid-fuel missile modelled on Russia's Iskander short-range ballistic missile system.
Some analysts said the new missile would be potentially capable of delivering warheads and striking targets within the entire Korean Peninsula, considering the range and capabilities of the Iskander and North Korea's recent advancements in missile technology.
The South Korean military official said the South Korean and US militaries are jointly analysing more details from the launch, including whether the missiles fired on Thursday were the same weapons the North tested on Saturday.
The latest launches came as US Special Representative for North Korea Stephen Biegun visited South Korea, and hours after the North described its firing of rocket artillery and an apparent short-range ballistic missile on Saturday as a regular and defensive military exercise.
North Korea also ridiculed South Korea for criticising those launches.
US president Donald Trump told reporters the weapons were smaller, short-range missiles, but:
"Nobody's happy about it."
He has met with Mr Kim at two summits but said at the White House on Thursday: