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The bodies of two deceased siblings, aged 6 and 10, have been found at a home in Perth's northern suburbs.
A woman, believed to be the children's mother, is under police custody in hospital.
WA Assistant Commissioner Paul Steel said the woman was arrested at a nearby beach carpark at about 8:40pm on Friday night.
"It appears that she has self-inflicted wounds that are non-life threatening," Commissioner Steel told reporters on Saturday.
"As a result, she is not able to be interviewed at this time.
"This is a tragic event and our heartfelt condolences go out to the friends and family of the children.
"Tragically for first responders, finding the bodies of two young children would have been a terrible thing to have to go through."Police were called to the Bogdanich Way property in Madeley at about 6:00pm on Friday, responding to calls from concerned neighbours.
Homicide detectives and forensic police will work at the crime scene in coming weeks to investigate the circumstances surrounding the deaths.
"I can assure the people of Western Australia, that the WA police are doing all that they can to investigate this matter and try and identify what it is that led to these tragic events," Commissioner Steel said.
The children's father is assisting with the investigation.
It is believed he was not at the home when the bodies were discovered.
"The scene is quite complicated, there are a number of witnesses that are helping police, that have information to provide," Commissioner Steel said.
"The children's father is one of those people who's actually with police and we're trying to assist with his welfare as well."
Commissioner Steel said the family was not known to police.
Part of Bogdanich Way was cordoned off as police searched the home and an evidence collection station was set up.
Police say they have no information to indicate there is any ongoing threat to the public.
WA Premier Mark McGowan described the events as "shocking, appalling, horrible, tragic" and said support would be provided.
"We'll make sure that there is support for children at the [victims'] school, psychological support and the like, but it's just one of those horrible, horrible things that sometimes occurs," he said.
"My thoughts go out to the family of the young girls."