The families of Damien Little and his wife Melissa have thanked the Port Lincoln community for its care and support over the deaths of Mr Little and the couple's two sons.
Ken and Sue Little, parents of Mr Little and Dale and Debby Goldsworthy, parents of Melissa, also thanked the police and other emergency services, and asked for time to grieve in private over Monday's tragedy.
Early that day Mr Little drove off a wharf in the Eyre Peninsula town killing himself and his two sons, Hunter, aged 10 months, and four-year-old Koda.
"In relation to our recent family tragedy, we would like to thank the SA Police Force, emergency and diving services and our local community as a whole on your care and support over the past two days," the statement released on Wednesday and reported online said.
It came as tributes continued to mount on the wharf including flowers, teddy bears and other items.
Flinders Ports, which operates the wharf, says it has no immediate plans to remove the shrine.
It has become the focus of the town's grief with hundreds of people, including family members and friends, continuing to visit.
On Tuesday, Mr Little's parents also revealed how their 34-year-old son had suffered from mental health issues over the past three years.
They said they had noticed the change in his personality and had tried to help him, without success.
The extent of his problems was not evident in two family photos released to the media.
In one, Mr Little and his wife Melissa are sitting on a beach with their two smiling young boys resting in their laps.
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14 or MensLine Australia 1300 78 99 78
