In a formal letter sent to Seoul, the North conveyed Kim's message that he felt "very sorry" for "disappointing" South Korean President Moon Jae-in.
In an editorial Friday, the Korea JoongAng Daily said it was "enraged at the North's abominable act".
The shooting of the man, a fisheries official who had gone missing this week, shocked South Koreans and sparked a barrage of criticism from the opposition and the public, prompting an unusually tough response from Moon, who called it "unpardonable".
According to the North Korean message, North Korean troops first fired blanks after the man found in the North's waters refused to answer other than saying he's from South Korea a couple of times.
But the North Korean side denied burning his body, saying the soldiers had burned a floatation device he was using in line with their anti-virus procedures, Suh said. After the 10 shots were fired, the North Korean soldiers approached to within about 10 meters from the floating material, but the South Korean was no longer visible on top of the material, the North Korean message read.
North Korea's leadership hopes the incident does not undermine recent efforts to foster trust between the neighbours, Suh cited the North's letter as saying, adding that Moon and Kim had exchanged letters this month in hopes of better ties. When they came near the floating object, they only found lots of blood but no sign of him.
Last week, South Korean police arrested a defector who they said had tried to return to North Korea by breaking into a military training site in South Korea's border town of Cheorwon. South Korea's National Intelligence Service said later Friday that Kim appeared not to have given the order to fatally shoot the South Korean official.
The North Korean message was sent from the United Front Department of the ruling Workers' Party, a top North Korean body in charge of relations with South Korea.
North Korean defector turned Seoul-based researcher Ahn Chan-il said it was "extremely rare for the North's supreme commander to offer an apology, especially to South Koreans and their President".
Moon praised Kim's "strong resolve to save lives" and steer virus control and flood recovery work in his September 8 letter, his office said.
Kim Jong Un apologized over the fatal shooting of a South Korean national by North Korean military personnel north of the border, a gesture that may help ease a new source of tension between the two rivals.