The Victorian Supreme Court jury determining if accused Bourke Street driver James Gargasoulas is mentally fit to stand trial has been discharged after failing to agree despite three days of deliberations.

The jury of eight men and four women began its deliberations on Monday afternoon, after a special hearing lasting more than a week which heard evidence from three mental health experts.

Mr Gargasoulas is charged with six counts of murder and 28 counts of attempted murder after allegedly "deliberately" driving his car at people in the lunchtime crowds in Melbourne's CBD in January last year.

His defence lawyers had argued he was mentally unfit to stand trial on the basis that he remained profoundly psychotic and was experiencing intrusive delusions due to his schizophrenia, which remained treatment-resistant.

The court previously heard the 28-year-old believed he was the second coming of Jesus Christ and needed to save the world from a comet.

The medical professionals who assessed Mr Gargasoulas all concluded he was not faking his mental illness.

The jury was unable to reach the unanimous decision required on his fitness to stand trial and, as a result, was discharged by Supreme Court Justice Lex Lasry today.

Justice Lasry has ordered that a certificate be prepared for Mr Gargasoulas to be treated in the secure mental health facility Thomas Embling Hospital.

The matter will be back before the court in late July.

In a statement, lawyer Genna Angelowitsch — who represents the families of five of those killed in the Bourke Street incident — said the delay to the justice process has come as a blow.

"The families of the loved ones killed in this tragedy are devastated by this further delay," she said.

"They hope the process can quickly move forward from here."

James Gargasoulas was charged with six counts of murder and 28 counts of attempted murder. ( AAP: Daniel Pockett, file photo )

Jury heard conflicting expert evidence

The jury was told that, under Victorian law, there is a presumption an accused is fit to stand trial unless, due to mental impairment, they meet any of the following seven criteria:

Unable to understand the nature of the charge

Unable to understand the nature of the charge Unable to enter a plea

Unable to enter a plea Unable to exercise their right to challenge jurors

Unable to exercise their right to challenge jurors Unable to understand the nature of the trial

Unable to understand the nature of the trial Unable to follow the course of the trial

Unable to follow the course of the trial Unable to give instructions to their legal practitioner

Unable to give instructions to their legal practitioner Unable to understand the substantial effect of evidence given against them

Two psychiatrists gave evidence that they had concluded Mr Gargasoulas was unfit to stand trial because they did not believe he could enter a plea for rational reasons, was not able to properly instruct his lawyers or understand the substantial effect of evidence given against him.

But a psychologist engaged by the prosecution told the hearing he had concluded Mr Gargasoulas was fit to stand trial, and did not believe he was incapable of carrying out the tasks set out under law.

Gargasoulas has 'delusional belief he's the saviour'

One of the psychiatrists, Lester Walton, who was engaged by the defence, told the jury Mr Gargasoulas was fixated on having the opportunity to espouse his delusional ideas in court.

"He initially said he's going to plead not guilty on the basis 'I'm innocent', and then he went on to say 'I wasn't in my right mind when I committed the offence, I want to plead mental impairment'," Dr Walton said.

"He's received advice that that is an option for him.

"Ultimately, he seems to be quite indifferent about what plea should be entered … all he's fixated on is that he has an opportunity to espouse his ideas."

Dr Walton said Mr Gargasoulas was confident he would be released from jail in 2020 regardless of the outcome of his legal proceedings.

Psychiatrist Andrew Carroll, who was engaged by the prosecution, agreed Mr Gargasoulas was unfit to stand trial as his decision-making process was underpinned by his "messianic delusional belief that he is the saviour".

Dr Carroll said Mr Gargasoulas was aware of the legal avenues available to him but was determined to plead not guilty so he had a public platform to espouse his ideas.

"He absolutely wanted to make sure he had a trial of some kind so he has a public platform," Dr Carroll said.

"His sense is, that if the jury is religious enough, they will find him not guilty.

"His delusional beliefs are of such a nature that he's unable to rationally weigh the options open to him."

Gargasoulas able to consider legal options: psychologist

But Mr Gargasoulas was also assessed by a third mental health expert — psychologist Michael Daffern, who was engaged by the prosecution — and his opinion was at odds with the other two witnesses.

Professor Daffern told the jury he had assessed Mr Gargasoulas as being fit to stand trial as he believed the accused killer was able to put aside his delusional thoughts in considering his legal options.

"Most importantly in my mind, Mr Gargasoulas understood that if he were found not guilty by reason of mental impairment that he would likely go to the Thomas Embling hospital," Professor Daffern said.

"Mr Gargasoulas did tell me that he wants to be recognised as the saviour, but he is also interested in … securing release at some point into the future."

Professor Daffern said Mr Gargasoulas believed that at the hospital "visiting would be better [because] he might be able to access the internet, that he might have access to a mobile telephone and he was also interested that there would be females at Thomas Embling hospital as well".

Professor Daffern also believed Mr Gargasoulas has narcissistic and anti-social personality disorders.

Each of the mental health experts who gave evidence were given access to the 6,500-page police brief of evidence, Mr Gargasoulas's Justice Health files, transcripts of phone conversations Mr Gargasoulas has had while in custody and letters he has written and received while in prison.