The attacker, identified by police as 40-year-old Joel Cauchi, was known to police in the neighboring state of Queensland, and police have spoken to his family after Saturday's attack, according to police from New South Wales and Queensland states.
Cauchi's family recognised him and contacted police on Saturday after seeing news reports of the killings.
"The family, when they viewed footage of the event on TV, thought that may well have been their son and they reached out to authorities," said Queensland Police Assistant Commissioner Roger Lowe.
The family said they were devastated by his actions, expressing condolences to the victims and the police officer who shot him dead.
"Joel’s actions were truly horrific, and we are still trying to comprehend what has happened," the family said in a statement. "He has battled with mental health issues since he was a teenager."
'Terrible scene'
Witnesses described how Cauchi, wearing shorts and an Australian national rugby league jersey, ran through the Westfield Bondi Junction mall with a knife.
He fatally stabbed six people and injured at least 12 before he was killed by Inspector Amy Scott, who confronted him solo while he was on the rampage.
Some shoppers and staff at the mall in Sydney's east tried to stop him and crowds sheltered in shuttered shops.
"This was a terrible scene," New South Wales Police Assistant Commissioner Anthony Cooke told reporters.
"There is still to this point nothing that we have, no information we received, no evidence we have recovered or intelligence that we have gathered that would suggest that this was driven by any particular motivation, ideology or otherwise."
Cauchi had recently moved to Sydney, the capital of New South Wales, from neighbouring Queensland. Police said they had searched a small storage facility he had been renting but found no major evidence to indicate an attack was coming.
He had been diagnosed with mental health issues when he was 17 and had been in contact with police frequently in the past four to five years, said Lowe of the Queensland police. Cauchi had not been arrested or charged with any crimes in Queensland, he added.
Cauchi led an itinerant lifestyle, had recently been sleeping in his car and had only infrequently stayed in touch with his mother via text messages, Lowe said.
Attacks such as Saturday's stabbing are rare in Australia, a country of about 26 million people with some of the world's toughest gun and knife laws.
Tribute grows
Five of the six people killed were women, police said on Sunday, while those taken to hospital with stab wounds included a nine-month-old baby, who was in a serious but stable condition.
The baby's mother, Ashlee Good, died in hospital from her injuries, her family said in a statement.
Faraz Tahir, a 30-year-old security guard at the mall who was the sole man killed during the attack, arrived in the country last year as a refugee from Pakistan, according to a statement from the Ahmadiyya Muslim Community of Australia, to which he belonged.
There was a heavy police presence on Sunday at the mall, which was closed to shoppers, with nearby streets cordoned off. A mound of floral tributes to the victims began to grow, with mourners arriving every few minutes.
"The individual stories of those who have been killed, the complete strangers rushing in to help as well as acts of courage and bravery mean that - whether you know the individuals who have been killed or not - you're grieving today," said New South Wales state Premier Chris Minns.
"The entire state will get behind those families in the days ahead as they recover and go through the inevitable grief of such a horrifying event."
Britain's King Charles, who is Australia's head of state, posted on the royal family's X account: "Our hearts go out to the families and loved ones of those who have been so brutally killed during such a senseless attack."
Prime Minister Anthony Albanese said he had received condolence messages from all over the globe, adding that the attack had highlighted the bravery of ordinary citizens.
"We have seen the footage of ordinary Australians putting themselves in harm's way in order to help their fellow citizens. That bravery was quite extraordinary," said on Sunday. "It's the best of Australians amidst this tragedy."