The KCNA news agency gave no details on the type of the weapon, saying only it had been developed over a long period.
This is North Korea's first official report of a weapons test in a year.
In a summit in June Mr Kim and US President Donald Trump agreed the Korean peninsula should denuclearise, but a detailed plan was never set out.
North Korean state media have provided no details as to what kind of weapon this was, but it comes shortly after a report based on satellite imagery identified the extent of North's complex network of missile bases around the country.
South Korea says it is in the process of analysing what the weapon is, but many have pointed out that the North made no commitment to halt any weapons development or shut down its missile bases.
Responding to the inspection, a US State Department spokesman said the US "remained confident that the promises made by President Trump and Chairman Kim will be fulfilled".
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