Before Tuesday's drill, the North Korea National Defense Commission sent a fax urging South Korean President Park Geun-hye to cancel the demonstration.
"North Korea called on South Korea to stop the live-fire artillery exercise, threatening grave consequences," Kim told the Yonhap News Agency.
The South Korean defense ministry's policy director replied and said the drill is legitimate, held in South Korean waters and is necessary to improve the Marine Corps' readiness.
North Korea did not take any action during Tuesday's drill, which took place on the Yeonpyeong and Baengnyeong islands and lasted an hour.
North Korea has previously spoken out against the drills, which South Korea holds every few months, the News Agency said.