North Korea's fourth nuclear test on Wednesday angered both the United States and China, which was not given prior notice, although the US government and weapons experts doubt the North's claim that the device it set off was a hydrogen bomb.
"The DPRK's H-bomb test ... is a self-defensive step for reliably defending the peace on the Korean Peninsula and the regional security from the danger of nuclear war caused by the U.S.-led imperialists," KCNA quoted Kim as saying.
"It is the legitimate right of a sovereign state and a fair action that nobody can criticize," he said.
Kim's comments were in line with the North's official rhetoric blaming the United States for deploying nuclear weapons on the Korean peninsula to justify its nuclear programme but were the first by its leader since Wednesday's blast.
The United States has said it has no nuclear weapons stationed in South Korea. But it has been in discussion with the South about deploying strategic weapons on the Korean peninsula after the test. Media said these could include nuclear-capable B-2 and B-52 bombers, and a nuclear-powered submarine.
Experts believe the test, which produced a seismic tremor of 5.1, too small to be a proper hydrogen bomb test, was designed to set the stage for a rare general meeting of its ruling Workers' Party, the first since 1980.
Kim noted the significance of the timing of the test as being held in the year of the party congress, "which will be a historic turning point in accomplishing the revolutionary cause of Juche," according to KCNA.
Juche is the North's home-grown state ideology that combines Marxism and extreme nationalism established by the state founder and the current leader's grandfather, Kim Il Sung.
KCNA said Kim made the comments on a visit to the country's Ministry of the People's Armed Forces.