The National Intelligence Service made the statement after British and Japanese news reports said that the 65-year-old reclusive leader could not walk more than 30 meters (yards) without resting and that he had undergone heart surgery.
Kim has heart disease and diabetes, but "there is no sign that the chronic diseases have deteriorated enough" to affect his public activity, the agency said during a briefing to local media reporters.
An agency official, who spoke on customary condition of anonymity citing office policy, confirmed the statement.
Kim's health has been a focus of international attention because his fate is believed to be tied to that of the isolated nation. Kim has ruled the North with an iron fist after his father and the North's founder, Kim Il Sung, died in 1994.
Kim has three known sons, but has not yet publicly designated any as his successor.