Authorities believe a man fatally shot his wife and four children, set their rural South Dakota house on fire, then turned the shotgun on himself, the state's attorney general's office said Tuesday.

Preliminary autopsy results show all six members of the Westerhuis family died of shotgun wounds. The bodies of Scott and Nicole Westerhuis and their children Kailey, Jaeci, Connor and Michael were found in the burned ruins of their home in Platte on Thursday.

South Dakota Attorney General Marty Jackley said investigators believe Scott Westerhuis fired all the deadly shots.

"It's hard for us to determine exactly if he started the fire, but that's the only thing that makes sense," Jackley's spokeswoman told The Associated Press.

A passer-by reported the blaze at the home near Platte early Thursday morning, but the fire chief said it was all but destroyed by the time firefighters arrived.

Authorities did not immediately name the victims, but the Platte-Geddes school superintendent has said Kailey was a third-grader, Jaeci a fifth-grader, Connor an eighth-grader and Michael a high school sophomore.

Jackley the "tragic loss" has affected the entire community of about 1,200 people who live in Platte, about 110 miles west of Sioux Falls.