A six-year-old girl and her parents have been shot dead while camping in Iowa, police have said.

The US state’s public safety department said the bodies of Sarah and Tyler Schmidt, both 42, and their daughter Lula were found in their tent in the Maquoketa Caves State Park.

A relative said the couple’s nine-year-old son, who was also on the trip, survived.

Authorities said the motive for the attack is unclear.

Suspected gunman Anthony Sherwin, 23, who was also staying at the campsite, was found dead in a wooded area of the park with a self-inflicted gunshot wound.

Mitch Mortvedt, assistant director of the Department of Public Safety’s division of criminal investigation said: “We don’t know what led up to this, what precipitated it.

“The investigation has not revealed any early interaction between the Schmidt family and him”.

Adam Morehouse, Sarah Schmidt’s brother, said the family had no connection to Sherwin.

“This was a completely random act,” Mr Morehouse said.

“This was just an individual who decided that morning to pick a tent and walk into it and execute the mission of what he wanted to do.”

Cedar Falls mayor Rob Green, who said he is a neighbour of the Schmidts, posted on Facebook on Friday that the couple’s nine-year-old son, Arlo, “survived the attack, and is safe.”

The post did not say whether Arlo was in the tent or even at the campsite when the shootings happened, and the mayor said he didn’t have those details.

Mr Morehouse confirmed Arlo was on the family’s camping trip, but said he did not know exactly where the boy was at the time of the shooting or know specifics about how it unfolded.

“He is with family, and he is OK, but I have not had any interaction with him,” Mr Morehouse said.

“As far as I know, he was uninjured physically.”

The killings prompted the evacuation of the park and camp ground, including a children’s summer camp.

After the evacuations, the suspected gunman was the only person unaccounted for, Mr Mortvedt said.

Officials did not say if he had a firearms permit, and provided no information about the gun used to kill the Schmidts.

Iowa allows people with permits to carry firearms virtually anywhere in the state.