On Saturday, North Korea fired two projectiles believed to be short-range ballistic missiles from its eastern coast into the East Sea, the fifth such launch since July 25, reports Seoul's Yonhap News Agency.
They flew around 400 km at a maximum altitude of 48 km, according to South Korea's Joint Chiefs of Staff.
The launch came shortly after US President Donald Trump said he had received another "very beautiful" letter from Kim.
After receiving a report on a new weapon system, Kim "gave an instruction to test it immediately" and "looked round the new weapon at the launching site", Pyongyang's Korean Central News Agency (KCNA) said in its report on Sunday.
It did not give further details on what type of weapon it was, only to state that the analysis of the test-fire result "proved that the new weapon system's advantageous and powerful demand of the design was perfectly met".
KCNA added that the new weapon was "developed to suit the terrain condition" and comes with a character "different from the existing weapon systems".
Pyongyang has claimed that it fired new tactical guided weapons in its July 25 firing and that it lobbed a newly developed large-caliber multiple launch guided rocket system in two subsequent launches on July 31 and August 2.
Following the latest firings, Trump wrote on Twitter on Saturday evening that Kim told him in a new letter that he wanted to resume the denuclearization talks once the joint exercise between the US and South Korea was over, and that its short range missiles "testing would stop when the exercises end".
The allies began their joint military drill last week, which the North has long condemned as a rehearsal for invasion.
( With inputs from IANS )