Afghan-Australian Saeed Noori, who has a history of drug abuse and mental problems, is accused of ploughing his car through a busy intersection earlier this month, careering into tourists and shoppers.
He has been charged with 18 counts of attempted murder, but now faces at least one murder charge after 83-year-old Antonios Crocaris, an Australian national, died from his injuries late Friday.
Six others remain in hospital.
"Homicide squad detectives are expected to upgrade one of those charges to murder."
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Nine foreigners were among those hurt, including from South Korea, China, Italy, India, Venezuela, Ireland, and New Zealand.
Police have alleged Noori made "utterances" to them about voices, dreams and the "poor treatment of Muslims" after his arrest, but no link to any terrorist group has been found.
The Melbourne Magistrates' Court heard on Wednesday that he may be suffering psychiatric issues or have an undiagnosed illness. He is due back in court on May 30.
Like other countries, Australia has been taking steps to prevent vehicle attacks in crowded public places since the Nice truck incident in southern France last year that killed 86 people.
They include deterrent options like fencing and closed circuit cameras, and using delaying tactics such as trees and bollards to slow down vehicles.
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