As public and political outrage grew in the South, the country's presidential office said in a statement that there were discrepancies in accounts of the incident and called for further inquiries.
South Korea's Defense Ministry said Thursday that the North had shot and burned a 47-year-old man's body after he disappeared from a government boat earlier in the week. He was reported missing while on duty on a fisheries boat near the island of Yeonpyeong, close to South Korea's sea border.
The government has said he may have been trying to defect to the North but his family have denied this.
The incident prompted an apology from Kim in a letter to South Korea's presidential Blue House on Friday, where he was quoted as saying he was "very sorry" for the "unfortunate incident that happened in our waters."
The letter also admitted that North Korea's military had fired blanks and later "ten rounds" of gunfire into the unidentified "intruder," as he did not reveal his identity and appeared to flee. It added that for safety reasons due to the coronavirus pandemic, they had burnt the floating device the official washed up on but did not find his body.
The message did not appear to placate his southern neighbors.
After a National Security Council meeting, South Korea's presidential office said that they had "decided to make the request to North Korea to conduct additional investigations and also request for a joint-investigation with North Korea, if necessary."
The two Koreas have never before conducted joint probes into previous incidents and have been technically at war since the 1950-53 Korean War ended in a truce.
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Earlier this week, South Korean President Moon Jae-in called the incident "shocking" and "very regretful," as it fueled anti-North sentiment and sparked a public backlash.
Moon's administration is facing pressure over how it responds to the incident, which coincided with a renewed push by Seoul for engagement with Pyongyang.
South Korea's main opposition People Power Party said on Saturday Kim's apology was not genuine and called on the Moon government to refer the case to the International Criminal Court.
The South Korean coast guard said Friday that their ships were searching the waters near the western sea boundary in case the official's body drifts back.
Several bloody inter-Korean naval skirmishes and deadly attacks have occurred there in the past. Seoul said it would strengthen surveillance and military preparedness in the west sea areas, to prevent a future recurrence.
Tensions were already high between the two countries, as Pyongyang cut off communication hotlines with the South this summer and dramatically demolished an inter-Korean liaison office set-up to foster better ties between the two.
North Korea has also lashed out at the South and North Korean defectors living there for propaganda leaflets and balloons that were parachuted into the clandestine communist country.
The Associated Press and Reuters contributed to this report.