Speaking to military officers while visiting the Ministry of People's Armed Forces, Kim said the test is "for reliably defending the peace on the Korean Peninsula and the regional security from the danger of nuclear war caused by the US-led imperialists".
"It is the legitimate right of a sovereign state and a fair action that nobody can criticise," KCNA news agency quoted Kim as telling the military officers.
He said the military should wage "a high-intensity struggle" to tackle scientific and technological problems in strengthening defence capability and rounding off combat preparations as well as "make many ultra-modern technological achievements conducive to building an economic powerhouse and improving the people's livelihood".
Kim again stressed on the need for the military to enhance offensive and defensive capabilities and stand combat ready to "resolutely counter any challenges by hostile forces".
The comments were the first by the North Korean leader after the country's announcement on Wednesday that it has successfully carried out its first hydrogen bomb test, or its fourth nuclear test.
While many expressed suspicion over North Korea's capability in successfully developing an H-bomb, the announcement has triggered international condemnation.