In a statement, the extended family said on Saturday they were devastated.
"They were a very socially aware family, doing their best to create a safe community, and that is why it is so shocking", she said.
"We respectfully ask that the community refrain from speculating on the circumstances surrounding this tragic incident".
He says Police found three firearms at the house, all licensed to 61-year old Peter Miles.
WA Police Commissioner Chris Dawson said: "I can only describe it as a horrific situation".
He emphasised that police did not believe anyone else was involved in the deaths and officers were not looking for any other suspects.
The police investigation is still ongoing to determine what had happened and the possible motive for the homicide. "We're providing him with as much support as we can".
The children were on the Autism spectrum, said a friend of the family, who is in the same home-schooling network.
Dawson refused to be drawn on who the person was that alerted police, their relationship to the victims or whether they heard gunshots.
Camera Icon The tragedy has rocked WA and the rest of Australia
They found three firearms at the scene all linked to grandfather Peter Miles and the bodies of the four children were recovered in a converted shed along with the body of a woman. "Forensic officers from police are completing their methodical work at the scene".
Mass shootings are not common in Australia, which has strict gun laws.
The shattered father of the four children killed in the Margaret River family shooting massacre says he still loves the man believed responsible for their deaths - their grandfather.
"I'm very confident as I stand here that the call and response that they made was exactly the same as what I would have done".
"Many people who know the family are deeply feeling the loss".
"This incident has shocked our local community to the core", said Pam Townshend, president of Augusta-Margaret River Shire, the district that includes Osmington, where the shooting occurred. I think he's been thinking this through for a long time, ' claimed Mr Cockman.
In a community so small and tightknit that some farms have just the first names of their owners painted on the driveway gates, it's a small, silent reference to a trauma that the entire area is still struggling to grasp. In this community we are so well connected.
"We will provide them with support, but they're both going as well as can be expected and I've got full confidence in them".
Peter had labored as a farmer and instructor and was previously the supervisor of the Margaret River Excessive Faculty farm.
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The magma that has emerged so far has been relatively cool and slow-moving, believed to be left over from a similar event in 1955. When you start seeing ferns go brown overnight, it's like, 'Wow, I gotta get out of here, ' he said.