The unnamed relatives of the Miles family said they were "still trying to understand how this could happen".
Katrina
Miles, her four children, and her parents Peter and Cynda Miles were
all found shot dead at their property in Osmington, near Margaret River.
Police confirmed they believe the killer to be among the dead.
Police
Commissioner Chris Dawson said they received a phone call from a man at
the property alerting them to the shootings early on Friday morning.
"I
wish to strongly emphasise that police do not believe any
other person
is involved in these crimes. Police are not searching for any other
suspects," he told reporters.
He said three firearms found on the property belonged to Peter Miles, 61.
Relatives
of those involved, in a statement issued through the police, asked
"that the community refrain from speculating on the circumstances around
this tragic incident".
Commissioner Dawson said the body of a woman was found in the house
on the rural property, while the bodies of a woman and four children
were found in a nearby converted shed where Ms Miles lived with her
children. A seventh person was found dead outside.
Local media report that Katrina Miles was aged 35, and had four children aged between 13 and eight.
The children's father had been notified of the killings and was "understandably grieving", Commissioner Dawson said.
Cynda
Miles, 58, and her family were said to have been active members of
their tiny rural community of Osmington, which is about 20km from
Margaret River, a popular tourist and wine-growing area.
Memorials have been posted on Katrina and Cynda's Facebook profiles. Image copyrightCynda Miles/FacebookImage caption
Cynda Miles was well known in her community
One neighbour, Felicity Haynes, described them as "lovely people".
"They
were a very socially-aware family - doing their best to create a safe
community - and that is why it is so shocking to think that could be
destroyed so quickly," she told the Australian Broadcasting Corp.
Pamela
Townshend, president of the Shire of Augusta-Margaret River, told
Fairfax Media: "It's sending shockwaves through the whole community -
we're all linked in one way or another, every family."
This is Australia's worst mass shooting since a massacre in Port Arthur, Tasmania, claimed the lives of 35 people in 1996.
That
incident led to comprehensive reform of the nation's gun laws, which
included a ban on automatic and semi-automatic weapons.