A man charged with murder after he allegedly ploughed his car through crowds of shoppers in central Melbourne has refused to appear in court.

Dimitrious 'Jimmy' Gargasoulas, 26, claimed he was feeling 'unwell' when summoned to Melbourne Magistrates Court on Monday to face five counts of murder.

His defence lawyer told the court that his client was unable to appear after being released from hospital following surgery on a gunshot wound to his arm.

The request was accepted by Magistrate Jelena Popovic, who also granted prosecutors more time to put together their evidence against Gargasoulas, the Sydney Morning Herald reports.

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Lawyers argued it would take months to put together all the documents required, calling the events in Melbourne last week "unprecedented."

Popovic remanded Gargasoulas in custody to appear again in August.

Gargasoulas had been questioned by police earlier on Monday after his release from hospital, where he was taken on Friday afternoon.

Gargasoulas was shot in the arm by police after he allegedly used a maroon Holden to run down 37 people on Swanston Street and Bourke Street in Melbourne's CBD on Friday last week.

Since then five of those people, including a 10-year-old and a three-month-old, have died and have been reflected in the charges.

Prosecutors say that more charges are likely to be laid as the case moves along.

Gargasoulas was taken to police headquarters about 12.30pm on Monday after Chief Commissioner Graham Ashton said Victoria Police had been waiting for permission from doctors to interview him.

A man believed to be Gargasoulas could be seen in a car, dressed in a hospital gown and facing away from cameras in 9 News footage.

Fifteen people remain in hospital after he allegedly rammed a mid-1990s Holden Commodore through one of Melbourne's busiest streets at 1.30pm on Friday.

Police at the scene near Flinders St station. Photo / AP
Police at the scene near Flinders St station. Photo / AP

Victorian Premier Daniel Andrews expressed his fears for two people who are fighting for their lives.

"We have grave fears for their health and wellbeing," he said on Monday.

"What occurred on Friday is not only a cause of great sadness, but it is a cause of legitimate and, I think, profound anger. All of us feel it."

Thalia Hakin, 10, Jess Mudie, 22, Matthew Si, 33, a three-month-old baby and a 25-year-old man died.

More than 30 were injured with 13 remaining in hospital on Sunday, with at least two of them still fighting for their lives.

"They are critical. They're in a very, very serious condition," Andrews told reporters.

"The fear is of course that the death toll from this evil act will rise.'

Thousands of Victorians and visitors laid flowers in Bourke St on Sunday as families paid tributes to their loved ones.

Police listen to witnesses at the scene. Photo / AP
Police listen to witnesses at the scene. Photo / AP

The Jewish community in St Kilda East held prayers for Thalia and all the other victims, praying for a speedy recovery for the injured.

Federal MP Michael Danby, who is Jewish, expressed his condolences.

"All Victorians can identify... with a girl who was going into grade five, her life all in front of her, robbed by some crazed person," he said.

Mr Si was a devoted husband and a loving father, brother and son, his wife Melinda said in a statement.

They had just finished lunch together in the city, and parted to go to their respective offices, when he was struck and killed.

"The family would like to thank everyone who helped Matt at the scene and did their best to save him," Si said.