The early afternoon smash on Thursday killed two men, injured a pregnant woman and caused traffic gridlock across the city.
Footage from bridge security cameras showed a northbound vehicle veering into southbound lanes about 1.40pm, triggering a series of collisions between three cars and a bus, police said.
Independent Sydney MP Alex Greenwich called on the government to review safety on the bridge and consider installing a centre divider in the wake of the fatal collision.
"I would hope that the government would seriously consider the need for a divider there," he said on Friday.
"Before anything is done, a proper safety-risk assessment needs to occur to ensure this doesn't happen again."
Asked about installing a physical barrier between oncoming vehicles, NSW Transport Minister Jo Haylen pointed to the bridge's contra-flow measures, which move lanes to manage traffic flow at different times of the day.
"This is a horrific, rare incident," she said.
"What's important here is that we allow the investigators to do their job and look into the circumstances of that horrific crash."
Two men died and a pregnant woman was injured in the multi-vehicle crash. (Dan Himbrechts/AAP PHOTOS)
Ms Haylen would not be drawn on the need for a centre divider and instead said drivers needed to stay alert and manage fatigue and mobile phone, alcohol and drug use.
Police are still investigating what caused the car to veer onto the wrong side of the road, killing its driver and that of the vehicle it struck.
A 51-year-old man driving a Hyundai i30 and a 44-year-old man driving a white Hyundai accent were both treated by paramedics but died at the scene.
Police have appealed for anyone with extra dashcam footage of the incident to come forward.
Acting Superintendent Clayton McDonald said it was rare for such a serious crash to happen on the Harbour Bridge considering the amount of traffic that passed across it daily.
He said police and Transport for NSW would review the incident, and a coroner could make recommendations.
The Sydney Harbour Bridge's contra-flow measures move lanes to manage traffic flow. (Dean Lewins/AAP PHOTOS)
No arrests have been made over the crash, although a motorcyclist was arrested after he allegedly drove through stopped traffic and into the cordoned-off crash scene.
The man, Ali Al-Robay, was refused bail in Downing Centre Local Court on Friday after Magistrate Clare Farnan viewed his "clearly concerning" traffic record.
His alleged actions on Thursday, past licence suspensions and non-compliance with restrictions, as well as a police pursuit, gave the magistrate no confidence he would comply with proposed bail conditions.
"I certainly accept that he had no idea the traffic was the result of a tragic fatality that occurred on the bridge a short time before," she said.
Al-Robay has been remanded ahead of another court appearance in a week.
Nine of the 12 charges he faces are fine-only offences and Al-Robay's barrister George Thomas said there would be some contest to charges of menacing driving and assaulting police.
He had expressed remorse in an interview with police and acknowledged the seriousness of his actions, the court was told.
