A 34-year-old man has been shot dead by police inside a packed shopping centre after a knife-point robbery and a carjacking in Sydney's west.

The man, a suspect in both crimes, was shot and fatally wounded after a brief struggle with a policeman in a private service corridor at Parramatta's Westfield mall.

Senior police said it appeared the man did not have a gun when he was shot, nor was it immediately clear if he had any other weapon.

"I'm not aware of this man being armed with a gun," NSW Police Assistant Commissioner Denis Clifford said in Sydney.

Homicide squad detectives will examine why the man was not subdued with a Taser stun gun or capsicum spray.

The drama unfolded after an armed robbery in Penrith, about 30km west of Parramatta.

Police cars began chasing a suspect from that robbery, who was in a stolen car, east along the M4 motorway, before the force's helicopter, PolAir, took over the pursuit.

The suspect's car crashed on the M4 shortly afterwards and the driver carjacked another vehicle.

The chase led to the Westfield mall, where a single male officer with more than 10 years' experience in the police force followed the suspect into the service corridor on level five of the mall.

The private corridor is in an area near a food court but shielded from the hundreds of shoppers in the area at the time.

"It appears there was a violent struggle, a confrontation," Mr Clifford said.

"And during that struggle the police officer discharged his weapon, fatally wounding the 34-year-old man."

Mr Clifford was unable to confirm a witness's report of five shots being fired.

The shooting comes one week after Brazilian Roberto Laudisio died after being shot with a Taser.

Mr Laudisio, 21, died in Sydney's CBD on March 18 after he allegedly resisted arrest.