Australian police said Monday they are investigating why a 40-year-old man with mental illness appeared to target women as he roamed a Sydney shopping mall with a large knife, killing six people and injuring a dozen more.

Videos shared on social media showed unshaven itinerant Joel Cauchi pursuing mostly female victims as he rampaged through the vast, crowded Westfield shopping complex in Bondi Junction on Saturday afternoon.

Five of the six victims killed were women, as were most of those wounded.

"The videos speak for themselves don't they, and that's certainly a line of inquiry for us," New South Wales police commissioner Karen Webb said.

"That's obvious to me, it's obvious to detectives, that that seems to be an area of interest -- that the offender had focused on women and avoided men," she told national broadcaster ABC.

Webb stressed that police could not know what was in the mind of the attacker.

"That's why it's important now that detectives spend so much time interviewing those who know him."

Cauchi's Facebook profile said he came from Toowoomba, near Brisbane, and had attended a local high school and university.

His parents say he had suffered from mental health issues since he was a teenager.

- 'Very traumatic' -

The last of Cauchi's six victims was identified Monday as Yixuan Cheng, a young Chinese woman who was a student at the University of Sydney.

The other women killed were a designer, a volunteer surf lifesaver, the daughter of an entrepreneur, and a new mother whose wounded nine-month-old baby is in hospital.

The mother, 38-year-old Ashlee Good, handed her bleeding baby girl to strangers in desperation before being rushed to hospital where she died of her injuries.

Her baby, named Harriet, is in a serious condition in a Sydney hospital but is expected to improve, health authorities said.

The only man killed was 30-year-old Pakistani Faraz Tahir, who had been working as a security guard when he was stabbed.

A total of eight people wounded in the assault remain in hospital -- some in critical condition -- after four were released in the past 24 hours, health authorities said.

Cauchi's assault, which lasted about half an hour, was brought to an end when solo police inspector Amy Scott tracked him down and shot him dead.

Scott -- hailed as a hero by police and political leaders -- was spending time with her family to deal with the "very traumatic matter", the state police chief said.

In a statement, Cauchi's parents offered thoughts for the victims and said their son's actions were "truly horrific".

"We are still trying to comprehend what has happened."

- 'Doing her job' -

The parents also sent a message to the officer who killed their son.

"She was only doing her job to protect others and we hope she is coping alright," they said.

Cauchi is believed to have travelled to Sydney about a month ago and hired a small storage unit in the city, according to police. It contained personal belongings, including a boogie board.

He had been living in a vehicle and hostels, and was only in sporadic contact with his family via text messages, his parents said.

A mound of flowers grew outside the Bondi shopping centre as people paid their respects to the victims.

Flags across the country flew at half-mast in mourning.

The Sydney Opera House is to be lit up with black ribbon in the evening.

Prime Minister Anthony Albanese said he had spoken to the families of some victims.

"The gender break-down is of course concerning -- each and every victim here is mourned," he told ABC radio, promising a "comprehensive" police investigation.

- Misinformation -

The prime minister also pointed the finger at people who spread false information about the attack.

"What social media has done is make everyone a publisher and some mainstream media also spread some misinformation," he said.

While some social media users falsely attributed the attack to terrorism, an Australian broadcaster had to apologise for wrongly identifying a 20-year-old student as the perpetrator.

A public coronial inquiry will be held into the attack, New South Wales state premier Chris Minns told reporters.

It will look into the police response and criminal investigation, but also the killer's past interactions with state health authorities, he said.