Two officers were patrolling Kings Cross at about 4am (AEST) on Saturday when they recognised a group of young indigenous men from Redfern in a stolen car on busy Darlinghurst Road.
As they approached the car, the 14-year-old driver saw the officers and tried to drive away, but the car mounted a crowded footpath and ran over a 29-year-old woman.
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The officers opened fire and hit the driver once in the chest and arm while an 18-year-old passenger was shot once in the neck.
NSW Police Association President Scott Weber said the officers did the only thing they could do to protect the community in a "pressure cooker" situation.
"Police officers acted with their training, with their skills and their instincts in a split second and they made the right decision," he told reporters in Sydney on Saturday.
But he said officers receive "no specific training" in regard to using guns against vehicles, saying the nature of policing is variable.
"There's not a set of rules for every set of circumstances," he said.
"It doesn't usually occur police officers are chasing a motor vehicle along a footpath."
It was impossible for officers to deploy a Taser as a moving car was involved in this situation, he said.
Four other males, aged 13, 14, 16 and 24, were in the back seat of the car at the time.
They were arrested and are assisting police with their inquiries.
The driver and passenger are in a serious but stable condition at St Vincent's Hospital and are expected to make a full recovery.
The 29-year-old woman who was run over and pinned by the car has chest injuries and is also being treated.
One of the officers had his foot run over and received treatment for minor injuries.
Assistant Commissioner Mark Murdoch said officers had been in touch with the Redfern community to fill them in on what happened.
"I would hope (the community) understands that we need to investigate exactly what happened and why it happened," he said.
More officers would be deployed in Redfern on Saturday night if the need arose, he added.
Mr Weber said he didn't believe the situation was directly linked to Redfern and was more a tragic set of circumstances.
"No police officer ever wants to draw upon their firearm," he said.
The officers involved had been sent home and were being assisted by the union, he said.
More than 50 shootings have alarmed Sydney in 2012 with most attributed to criminal organisations and gangs.
On Friday, the NSW government banned Bikie gangs owning tattoo parlours and wearing their colours in licensed Kings Cross venues after two drive-by shootings in north-west Sydney hours earlier.
Police believe the attacks are part an ongoing dispute between rival gangs the Hells Angels and Nomads.
Police officers have also been involved in the gun violence.
Ryan Pringle, who was armed with a knife and a crossbow, was tasered by police before they shot him dead in northern NSW on Monday.
On March 25, a senior police officer shot and killed 34-year-old Darren Neill at the Westfield Shopping Centre at Parramatta.
Mr Weber said police welcomed the new laws but said more officers and resources were still needed to target criminal gangs.
