Greenwood County Sheriff Tony Davis said that deputies received a call at around 6 pm Tuesday from a man inside the home who said he was intent on "hurting himself," according to FoxCarolina.com.
Sheriff's Department spokesman John Long said that while deputies were on their way to the scene, they received a 911 call from a neighbor saying two more children had arrived at her home and told her shots had been fired in the house.
Davis said that the shooter was among the dead and there was no further danger to the community.
"I've been in law enforcement in Greenwood since 1975 and to my knowledge this is the first (situation) that I responded to with this many deceased," Davis said.
Long said that the shooting appeared to stem from a domestic dispute. The bodies were discovered by a SWAT team that entered the house after failing to make contact with anyone inside.
The sheriff said that two of the adults in the home appeared to be a couple and the two children were around 10 years old.
Greenwood, a town of approximately 70,000 people, is located 80 miles west of South Carolina's capital, Columbia.