A man shot and killed his family of seven, including five children, then turned the gun on himself, US police said Thursday.

Officers in the small Utah town of Enoch City found eight bodies - one of them that of a four-year-old - after being called by friends and relatives who were concerned for the family.

A spokesman for Enoch City said police had discovered three adults and five children at a single-family home, all dead from what appeared to be gunshot wounds.

"Evidence suggests that the suspect took his own life after killing seven others in the home," a statement from the town said, naming him as 42-year-old Michael Haight.

The dead were his wife, her mother, and the couple's five children - three girls and two boys aged between four and 17.

An investigation is under way but police said they were not looking for anyone else in connection with the crime.

Enoch is a rural town of around 7,000 people in the southwest of Utah. It sits about three-and-a-half hours' drive from Salt Lake City.

The state is known as the headquarters of the Church of Jesus Christ of Latter Day Saints, popularly known as Mormons, a conservative Christian sect that places strong emphasis on family, but which historically encouraged polygamy.