Australian police have identified a 40-year-old man who suffered from mental illness as the perpetrator of a Sydney shopping center stabbing rampage that killed six people and left several more in critical condition.

New South Wales police Assistant Commissioner Anthony Cooke said Sunday the man had come from the northeast state of Queensland and was known to law enforcement. 

"There is still to this point nothing that we have, no information we have received, no evidence we have recovered, no intelligence that we have gathered that would suggest that this was driven by any particular motivation, ideology or otherwise," said Cooke. 

"We know that the offender in the matter suffered from, suffers from, mental health." 

The 40-year-old man -- who was shot dead by a senior police officer at the scene Saturday -- was named as Joel Cauchi.

A Facebook profile said he came from the Toowoomba, near Brisbane, and had attended a local high school and university.

A distinctive grey, red and yellow dragon tattoo on his right arm was used to help identify him. 

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

Police are still trying to understand whether those attacked were chosen at random. 

Five women and one man were killed during Cauchi's Saturday afternoon rampage, which took place in a bustling shopping center in Sydney's Bondi Junction neighbourhood, not far from the famed beach.

Among the injured was a nine-month-old baby girl who was said to be in a "serious but stable condition in hospital".

The baby's mother is believed to have succumbed to her injuries after desperately passing the child to strangers in the hope they could save the newborn's life.   

Two of the victims are said to have no family in Australia and attempts are being made to contact the relatives overseas.

Prime Minister Anthony Albanese said Australians -- who are largely unaccustomed to incidents of violent crime -- were struggling to understand an "unspeakable" attack that is "really just beyond comprehension".

"People going about their Saturday afternoon shopping should be safe, shouldn't be at risk. But tragically, we saw a loss of life, and people will be grieving for loved ones today," he said.

"We also know there are many people still in hospital dealing with recovery, and our thoughts and prayers are with them."

Albanese said he had received messages from US President Joe Biden, British Prime Minister Rishi Sunak, and New Zealand Prime Minister Christopher Luxon among others. 

He again hailed the officer who shot Cauchi dead as a hero.

The "wonderful inspector", he said "ran into danger by herself... without thinking about the risks to herself."

Outside the shopping centre early on Sunday, a collection of flowers started to build. 

One white ribbon wrapped around a bunch of flowers simply said "RIP" with a heart drawn in black marker.

Families embraced as they lay flowers. One man stood silently and wiped away tears, before moving on.

Sydney resident Paul Hoolahan said he came to pay his respects to those who died at the shopping centre, where he often has coffee with his grandkids.

"It is emotional," Hoolahan told AFP. "It shouldn't happen. It hit here,” he said pointing to his chest.