The man accused of running down pedestrians along Bourke Street in Melbourne's CBD and killing six people has pleaded not guilty to murder and attempted murder charges.

James Gargasoulas, 27, appeared via video link for a brief hearing at the Melbourne Magistrates' Court to enter the plea to six counts of murder and 28 counts of attempted murder as well as other charges.

It means the case will go directly to the Supreme Court without a pre-trial hearing before a magistrate.

Mr Gargasoulas is accused of driving a car through the busy Bourke Street mall and along the footpath for several blocks on January 20, hitting and killing six people and injuring many others.

He barely spoke throughout the short hearing other than to confirm he understood the charges and to enter his not guilty plea.

Defence lawyer James Yianoulatos told the hearing that Mr Gargasoulas' fitness to plead was a live issue.

Under Victorian law, a person may be found unfit to plead if it is determined they have a mental disorder or impairment and therefore do not understand the charges they face and the nature of a criminal trial, and cannot give instructions to their lawyers.

Mr Gargasoulas will face a hearing in the Supreme Court on Monday where a timetable will be set down for the case.

A photo of 10-year-old Thalia Hakin was one of the many tributes placed along Bourke St. ( ABC News: Patrick Rocca )

Three-month-old Zachary Bryant, Thalia Hakin, 10, Matthew Si, 33, Japanese student Yosuke Kanno, 25 and Sydney woman Jess Mudie, 22, were all killed after being hit along Bourke St.

Bhavita Patel, 33, died in hospital 10 days later.

Mr Gargasoulas has been in custody since his arrest on the day of the attack.

The family of some of the victims were in the Melbourne Magistrates' Court for Friday's hearing.