Updated 7.15am

In the midst of a Sydney mall stabbing rampage, witnesses say a fatally wounded mother handed over her injured nine-month-old baby to a stranger to save the infant's life.

Stories of courage are still emerging from Saturday's attack, in which a 40-year-old knifeman with mental illness roamed the packed shopping centre, killing six people and seriously wounding a dozen others.

Lone senior police officer Amy Scott is being hailed for tracking down, and then shooting dead the assailant during his killing spree.

One young man was filmed fending off the attacker on an escalator, armed only with a shopping centre bollard.

Storekeepers opened their doors to shelter frightened shoppers.

But the harrowing story of 38-year-old mother Ashlee Good's desperate final act to save her baby daughter Harriet has struck a chord with many shocked Australians.

Witnesses told local media she was heard screaming when the assailant approached her in the shopping complex.

"The baby got stabbed," one man at the scene with his brother told Channel 9 News in the aftermath of the attack.

"The mum got stabbed and the mum came over with the baby and threw it at me," he said.

Within hours of the attack, police said the toll had climbed to six after Good died in hospital.

Her baby is still in "a serious but stable condition" in hospital, New South Wales police assistant commissioner Anthony Cooke said Sunday.

In a statement to Australian media, Good's family described her as "a beautiful mother, daughter, sister, partner, friend, all round outstanding human and so much more".

"To the two men who held and cared for our baby when Ashlee could not -- words cannot express our gratitude" the statement said.

The child, they said, was "doing well" after "hours of surgery".

Sky News Australia television reporter Laura Jayes was near tears as she revealed on air that she knew the sixth victim, who she described as an "incredible athlete".

"I can tell you that it was a mother, a mother in the prime of her life, a new mother with a nine-month-old baby," Jayes said.

"I can't imagine her needing to hand over the most precious thing in her life."

"Her baby went to surgery and her mum didn't make it. So that's really hard news to take. And I am bringing you that not knowing about the other five victims. But there's one victim I do know about. And it's just so cruel."

Prime Minister Anthony Albanese praised the courage displayed by "ordinary Australians" in the attack.

'In harm's way'

"We also see the footage of ordinary Australians putting themselves in harm's way in order to help their fellow citizens," he told reporters Sunday.

"That bravery was quite extraordinary that we saw yesterday, the best of Australians amidst this extraordinary tragedy."

One short video widely circulated on Australian media showed a young man in a white T-shirt fending off the attacker on an escalator, armed only with a bollard. It did not show how the confrontation ended.

Many people praised shopkeepers who gave them shelter in the midst of the rampage.

Albanese singled out the "wonderful" police inspector - named in local media as Amy Scott - who shot and killed the offender.

She "ran into danger by herself and removed the threat that was there to others without thinking about the risks to herself", the prime minister said.

An unidentified middle-aged witness at the scene told national broadcaster ABC he saw the shooting.

"All I heard was 'put it down'. And then she shot him," he said.

"If she didn't shoot him, well he would have kept going. He was on the rampage. He was on a bloody rampage. And then she walked over and was giving him CPR."

Police said the senior officer was near the shopping centre when the stabbing unfolded and was guided to the gunman's location by people there.

"She took the actions that she did, saving a range of people's lives," said New South Wales police Assistant Commissioner Anthony Cooke.

"She was on her own."

Family of attacker offer 'condolences' to victims

Australian police on Sunday said the parents of a man who killed six people in a Sydney shopping centre had offered condolences to their son's victims and their families.

Queensland police assistant commissioner Roger Lowe said the parents of the man had also sent a message of "support" to the officer who shot him dead, "expressing their concerns for her welfare."

The 40-year-old attacker has been named as Joel Cauchi, an itinerant with a history of mental health problems.

Lowe said Cauchi had been diagnosed with an unspecified mental illness at age 17, but police were still trying to establish what prompted a violent change in his behaviour. 

He is said to have been in contact with police several times over the last four to five years but has never been arrested or charged with any offence.

Cauchi is said to have had limited and sporadic contact with his parents since moving to Sydney, with contact limited to occasional text messages.

"We believe he has been sleeping in a vehicle or backpacks (hostels)" Lowe said. 

Police are investigating whether Cauchi had targeted women specifically, but he is not believed to have any religious, ideological or terror motive.

Five of his victims who died were women, and one was a male security guard.

"He has not been prosecuted or arrested or charged for any offence within Queensland. And he has no record within the courts for a domestic violence order" Lowe said. 

Queensland police indicated they had not been tracking him or did not perceive him as a threat to society. 

"We have people in our society who suffer from mental health, they go about their days without trouble without causing these types of crimes" Lowe said. 

"Mental health in society is not a crime," he said. "We do not run an intelligence regime on persons who suffer from mental health."

"There would only be an exchange of information if a person were to present such a security risk in society."