An officer was confronted with a "terrible dilemma" before he shot dead a woman in her 20s who was stabbing her mother, police say.
Victoria Police Acting Superintendent Scott Colson stood by the officer's actions on Saturday, saying the man and another officer were called to Lower Plenty in Melbourne's northeast about 6.30pm on Friday.
They arrived at the home of neighbours who mistakenly believed the woman, aged 26, had lit her mother on fire.
Instead, the officers soon saw the young woman over a fence, stabbing her mother with a knife.
The officers asked the woman to stop and drop the knife but she kept stabbing, Supt Colson said.
One of the officers then shot the daughter and she died at the scene.
By the time of the shooting, the woman's mother had already died after she was stabbed in the torso and neck, Supt Colson said.
The mother was aged 53.
"From what I know from attending the scene last night, they were confronted with a terrible dilemma and they've acted absolutely appropriately, within their training and within the guidelines," Supt Colson told reporters on Saturday.
"They have my full support along with the broader organisation."
Supt Colson said he did not know how many shots were fired.
He said neither of the officers had or were required to have Tasers.
The officer who shot the daughter dead had about four years' experience and his colleague about six.
Supt Colson said the man was left with no choice but to shoot the woman.
The homicide squad, under oversight from Victoria Police's professional standards command, would investigate the incident, he said.
The daughter was on bail for an irrelevant matter at the time of her death, and someone unrelated to her family had an intervention order out against her.
The incident happened at the mother's home but there was no court order stopping the daughter from being there.
"The members were surrounded by and given as much support as we can yesterday," Supt Colson said.
"They were feeling it tremendously ... they don't go to work expecting to draw their firearms and be involved in these sorts of tragedies."
Supt Colson described the women's deaths as a tragedy.
