Officers were dispatched Tuesday night to the home in Callison, S.C., just south of Greenwood, after a man called the sheriff's department and told them he was going to kill himself, then disconnected.
Before police arrived, another caller said shots had been fired and that the children were running away from the house.
Four of the children fled to the second caller's neighboring home and were unharmed.
The six dead ranged in age from 9 years old to early 50s. The gunman was later identified as 27-year-old Bryan Sweatt, who was dating one of the people in the home.
A SWAT team entered the home after failing to negotiate with the original caller. There, they found the bodies, all with gunshot wounds. All six died from gunshot wounds, said Greenwood County Sheriff Tony Davis.