He was later found dead with a gunshot wound to his head in an apparent suicide.
A hunting rifle was found on the 50-year-old gunman's body about 4 kilometers (2.5 miles) from the store, located in Sejong City, Lee Ja-ha, head of the Sejong Police Agency, said in a televised briefing. Another rifle was found in his vehicle, which was parked about 100 meters (yards) away from the body, he said.
The other dead were a father, 74, and son, 50, linked to the family that owned the store, and another man, 52, who'd been living with the elder man's daughter, Lee said. Sejong City is 120 kilometers (75 miles) south of Seoul, the capital, and is home to some of South Korea's government agencies and ministries.
The suspect shot the son as he sat in a car in front of the store and then entered a house next to the shop and shot the father, police said. In the store, the suspect then shot the other man before pouring paint thinner on the floor and setting the shop ablaze.
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The gunman had gotten the rifles from a police station in the nearby city of Gongju in the central part of South Korea about two hours before the morning shooting, Lee said.
Shooting incidents are rare in South Korea, which tightly controls gun possession, although there has been a spate of shooting deaths among soldiers. Every able-bodied South Korean man has to serve about two years in the military because of tensions with rival North Korea.