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A 10-year-old girl was also present during the incident, which occurred at a home on Kellaway Crescent in Mill Park about 7.50pm yesterday, but she managed to escape the scene and avoid physical injury.
Victoria Police Homicide Squad Detective Inspector Dean Thomas said police believed the man and woman involved are husband and wife, with the two girls being their children.
Detective Inspector Thomas said it was believed police had attended the address about 12.50pm yesterday to do a psychiatric assessment.
“A person at the address was assessed at that time,” he said.
Detective Inspector Thomas said the person was cleared.
A neighbour then called emergency services to the home about 7.50pm.
Police found a 39-year-old woman with stab wounds. She died at the scene.
Detective Inspector Thomas said police then found a 40-year-old man at the scene, who “proceeded to injure himself” after speaking to police.
Police took immediate action to detain the man and he was treated at the scene.
Detective Inspector Thomas said a six-year-old was later found critically injured inside the home before she died at hospital.
The man is under police guard in hospital in a critical condition.
Detective Inspector Thomas said the man was known to police and that police were not looking for anyone else in relation to the incident.
He said blood seen at a neighbouring property had been caused by the injured woman running to seek help before she was “pursued by the offender”.
He said it was too early in the investigation for police to state the motive behind the “terrible, traumatic incident”.
Anyone with information or dashcam footage from the area at the time of the incident should call Crime Stoppers on 1800 333 000.
If you need help in a crisis, call Lifeline on 13 11 14. For further information about depression, contact beyondblue on 1300224636 or talk to your GP, local health professional or someone you trust.