A knife-wielding man who killed six people in a Sydney shopping centre before being shot dead has been identified by Australian police.

Joel Cauchi, 40, sent the crowded Westfield Bondi Junction complex into panic on Saturday when he began stabbing people with a long blade.

Five women and a man died. Several others, including a baby, were injured.

Authorities said the attack was most likely "related to the mental health" of Mr Cauchi.

Asked whether she believes he was targeting women, New South Wales Police Commissioner Karen Webb told reporters on Sunday it would be "an obvious line of inquiry".

But she added she would not describe the stabbings as an "act of terror", reiterating that police believed there was "no ideological motivation".

Mr Cauchi was previously known to police but had never been arrested or charged in his home state Queensland. He had lived itinerantly for several years and was first diagnosed with a mental illness at 17, Queensland Police said.

His family described his actions as "horrific" and said he had had mental health issues "since he was a teenager", in a statement released through Queensland Police.

The Cauchi family said: "We are absolutely devastated by the traumatic events that occurred in Sydney yesterday.

"Our thoughts and prayers are with the families and friends of the victims and those still undergoing treatment at this time.

"Joel's actions were truly horrific, and we are still trying to comprehend what has happened."

They added they were in touch with police and had "no issues" with the officer who shot Mr Cauchi.

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

Initial searches of a small storage unit Mr Cauchi owned in Sydney had not shed light on a possible motive, NSW Police said.

Authorities said they were still trying to notify families of the victims, noting two appeared to have no relatives in Australia.

But the family of Ashlee Good - the injured baby's mother - say she was among those killed. Witnesses have told local media that Ms Good desperately passed the infant to bystanders in the moments after she was wounded.

"The mum got stabbed and the mum came over with the baby and threw it at me and (I) was holding the baby," one man told Nine News.

The nine-month-old girl "had surgery overnight and is currently in a critical condition and is in ICU," Health Minister Ryan Park told ABC news.

"Now, we certainly are hoping that she gets through this but there is a long way to go."

Ms Good's family said they were "reeling from the terrible loss of Ashlee, a beautiful mother, daughter, sister, partner, friend, all-round outstanding human and so much more".

"We appreciate the well-wishes and thoughts of members of the Australian public who have expressed an outpouring of love for Ashlee and our baby girl," the family said in a statement on Sunday.

Another victim was Faraz Tahir, a 30-year-old man from Pakistan who had sought refuge in Australia a year ago, according to the Ahmadiyya Muslim Community of Australia.

Mr Tahir was a security guard and "cherished member" of the local community "known for his unwavering dedication to kindness", a statement said.

Dawn Singleton, 25, also died, her employer White Fox Boutique said. "We are all truly devastated by this loss. Dawn was a sweet, kind-hearted person who had her whole life ahead of her. She was really amazing," the company wrote online.

Prime Minister Anthony Albanese said Australians were "waking up to try to deal with the shock and trauma" of what had happened.

Describing the attack as "unspeakable and really just beyond comprehension", Mr Albanese again praised the actions of a lone senior policewoman who confronted Mr Cauchi and shot him dead as horror gripped the mall.

"The wonderful inspector who 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, thanking her and emergency teams.

Police identified her on Sunday as Inspector Amy Scott, adding she had no current plans to speak publicly about the incident.

Others have also been heralded for their bravery - including a man clutching a bollard who was filmed staring down Mr Cauchi on an escalator.

Authorities said nine people had been taken to hospital after the stabbings, and another three people had sought medical attention overnight. About 40 paramedics were initially involved in the response.

The shopping centre in Sydney's affluent east remained closed on Sunday and forensic investigators pored over the scene.

By mid-afternoon several hundred bouquets of flowers had been placed close to the entrance, on Oxford St.

Many of those leaving tributes walked away in tears. Several volunteers in bright green vests marked "mental health" have been on hand to speak to anyone feeling they need support.

Among those laying flowers was Yvonne Russell, who has lived in the area for 35 years. "I'm shocked," she tells the BBC. It's very confronting and trying to process it. This is our backyard. We work Monday to Friday then go shopping on Saturday, so it could easily have been us."

Many world leaders have also expressed shock. New Zealand leader Christopher Luxon said all New Zealanders were thinking of those affected, while UK Prime Minister Rishi Sunak said they were "in the thoughts and prayers of the British people".

Pope Francis said he was deeply saddened by the "senseless tragedy" and offered prayers. King Charles added he and Queen Camilla were "utterly shocked" and "our hearts go out to the families and loved ones".