The family of the Sydney mall stabber recognised their son was the killer from TV footage of the attack, police say.
Joel Cauchi killed six people with a knife as he rampaged through the Bondi Westfield on Saturday.
Footage from the scene showed Cauchi chasing victims down before he was shot by a police officer inside the building.
Now his family have released a statement saying his actions were "truly horrific".
Speaking to media on Sunday afternoon, Queensland Police Assistant Commissioner Roger Lowe said Cauchi's family had reached out after seeing footage of the attack on television.
Police had spent Saturday evening with the family collecting information, he told reporters.
"The family have cooperated with the Queensland police service in this regard and they are issuing a statement on their behalf with respect to their own condolences and thoughts to the family and friends of those victims involved in this tragedy," he said.
"Equally they have sent a message to the NSW police force with respect to support of the police officer who has killed their son and expressing their concerns for her welfare."
He described Cauchi as "itinerant" and said his family didn't have regular contact with their son.
"It is periodic contact where he may respond to a text message," Lowe said.
"He would periodically text his mother to say where he was."
He added Cauchi had been diagnosed with a mental illness at the age of 17, and his mental health had been in decline.
Cauchi family's full statement
"We are absolutely devastated by the traumatic events that occurred in Sydney yesterday," it reads.
"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. He has battled with mental health issues since he was a teenager.
"We are in contact with both the New South Wales Police Force and Queensland Police Service and have no issues with the Police Officer who shot our son as she was only doing her job to protect others and we hope she is coping alright."
