The 29-year-old died at the Mount Druitt Westfield in Sydney's west on Saturday afternoon with the officers involved in the incident hailed for their actions.
On Sunday, Assistant Police Commissioner Gavin Wood said six women aged in their mid 20s had crossed paths in the car park at 3.15pm and a brawl had erupted.
The women were not known to each other and it was "sheer fluke that they have met", he said.
The husband of one of the women retrieved a large machete from his car and was walking towards the women when police intervened.
"Police asked the male to drop the machete," Mr Wood said.
The man refused, and continued to walk towards the women.
"The police officers got in the middle between the deceased person who was carrying a large machete and some of those females subject to the melee," he said.
"At that stage, the police officer fired his service revolver".
Mr Wood had checked CCTV footage and the officers' body-worn video and was "content with the actions of the police".
The shooting would be subject to scrutiny but he said "their actions were commendable … they were brave".
"We will put our arms around those police as we do, and they deserve that," he said.
"They are good people, they are good police officers. They didn't come to work yesterday knowing they had to shoot somebody."
Mr Wood said he had spoken to both officers and they were upset, and the enormity of what happened had started to set in.
The shooting was declared a critical incident. The investigation will be overseen by the police law enforcement commission and professional standards and led by the homicide squad.
The man, a father of two young children, did not have an extensive criminal history and no gang affiliations.
Mr Wood said the machete he was carrying was at least 50 cm long.
"If anyone had seen it, you'd be alarmed simply by the vision of it," he said.
The man's wife was arrested but later released, subject to further police inquiries.
The actions of the six woman involved in the incident will also form part of the police investigation.