Three people remained critically ill in hospital after the Australian-Afghan driver ploughed through a busy downtown intersection in his car on Thursday in what authorities said was a "deliberate act".
The 32-year-old, who came to Australia as a refugee, has a history of drug abuse and mental problems and Prime Minister Malcolm Turnbull reiterated that officials had established no terrorism link "at this stage".
"To be attacked like this, in the middle of one of our great cities, is a shocking event, a shocking crime," Turnbull said.
"He has said, in a number of what the police are describing as utterings, that he attributed his actions to perceived mistreatment of Muslims.
"But at this stage, because investigations are continuing, apart from that statement, there are no known links to any political issues, or any links to extremist groups, and I am advised at the moment that no terrorism link has been identified."
But he added that "a mass of material" was being investigated and "nothing should be ruled out".
The man, who was wrestled from the car by an off-duty police officer, was due to undergo a psychiatric assessment later Friday and is yet to be formally interviewed.
He was widely identified in the Australian media as Saeed Noori.
Police said nine foreign nationals were among those hurt, including three South Koreans. Two of them -- men aged in their 60s -- are among the critically hurt.
Police said the other overseas victims came from China, Italy, India, Venezuela, Ireland, and New Zealand, with the city full of tourists for the festive season.
Boosted police presence
"We should always be cautious, but we're not going to be cowed or intimidated by cowardly acts of individuals who seek to do us harm in public spaces, like this," he said.
Melbourne began returning to normal on Friday, with roads reopened.
But there was a boosted armed police presence, with a major carols by candlelight event scheduled for Christmas Eve and the Boxing Day cricket Test between Australia and England taking place nearby.
Thursday's incident came after a car rammed into pedestrians in Melbourne's busiest mall in January, killing six people. The driver, whose case is still being heard in court, was a drug addict and had allegedly just stabbed his brother.
Canberra has become increasingly worried about homegrown extremism and officials say they have prevented 13 terror attacks on home soil in the past few years.
After the Nice truck attack in southern France last year that killed 86 people, Australia unveiled a strategy aimed at preventing vehicle attacks in crowded public places.
Suggested steps included deterrent options like fencing and closed circuit cameras, and using delaying tactics such as trees and bollards to slow down vehicles.
Melbourne has also been installing a public siren system and more security cameras to warn people of a possible terrorist attack or other serious threats.
Turnbull said implementing the measures was a matter of "high priority", but admitted it was impossible to "protect every crowded place, from every vehicle".
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)