Police say they are looking for two Caucasian males in their late teens to early 20s.
The driver of the green vehicle turned into Bourke Street Mall from Swanston Street after officers flashed their lights and tried to get him to pull over.
One officer got out of his car and drew his firearm as the car hit a security bollard in the pedestrian mall, before determining that the driver was attempting to evade police and not harm pedestrians.
His passenger escaped on foot, while the driver performed a U-turn before heading back towards Swanston Street.
The car was later found dumped in the underground car park of a residential building in Albert Park after a member of the public tipped off police. When police found the car, the plates had been removed.
Assistant Commissioner Luke Cornelius on Friday morning said police knew who the plates were registered to and the identity of the registered owner of the early model Lancer.
The secure car park where it was found dumped could only be accessed by fob entry.
“Either someone has let that vehicle in, or the person driving the vehicle has been able to access that car park by way of a fob,” he said.
Mr Cornelius said on Friday that police would release photos of those who they believe are involved in the incident if needed, but did not want to do so pre-emptively as it could contaminate the recollection of witnesses.
He said there were some “active and strong lines of inquiry” and called on the two men to hand themselves in.
The incident reignited community concern after two murderous attacks within the past four years claimed the lives of seven people on the same shopping strip in the heart of Melbourne.
The driver had dark, short hair and was wearing a baseball cap and white golf-style gloves at the time.
Anyone with footage or who witnessed the incident is urged to call CrimeStoppers on 1800 33 000.
Simone is a crime reporter for The Age. Most recently she covered breaking news for The Age, and before that for The Australian in Melbourne.