The crime scene at Westfield Parramatta.

The crime scene at the Parramatta shopping centre. Photo: twitter.com/@grantshow

POLICE shot a 34-year-old man dead in a crowded shopping centre after a dramatic car chase across western Sydney.

Last night police said the man had been pursued from Penrith to Parramatta, where he was shot in a secluded hallway outside the food court at Westfield Parramatta.

''It appears that there was a sequence of events that started early this afternoon with what was an alleged robbery at knifepoint in the Penrith area that led to a pursuit of an alleged stolen vehicle by police down the M4,'' said Assistant Commissioner Denis Clifford from the north-west metropolitan command.

Assistant Commissioner Clifford said police stopped the pursuit after they were able to get a helicopter to track the car. But the car was involved in a collision on the M4.

''It is alleged that the driver of that vehicle was then involved in a violent car-jacking of a second vehicle which sped away from that scene,'' Assistant Commissioner Clifford said.

The police helicopter pursued the second alleged stolen car to Parramatta, where it was driven into the car park of the Westfield shopping centre.

The man was pursued through the shopping centre until he was shot by a lone officer in an area just outside the food court.

''I must say I was horrified when I was first briefed that this may have occurred in the food court but I can say now this is not the case,'' Assistant Commissioner Clifford said. ''It was away from the public.''

The officer who shot the man had not yet been identified but had more than 10 years' experience. He had not been interviewed.

A Herald reporter, Richard Blackburn, witnessed an earlier car chase on the M4. Blackburn was on the motorway about 3.30pm when he saw a citybound blue Mitsubishi Triton swerving through traffic.

''He would have been doing at least 140 km/h. He was going at a fair old rate,'' Blackburn said.

An investigation into the shooting has begun. It is being overseen by the professional standards command and includes officers from the homicide squad.