The jury determining whether accused Bourke Street driver James Gargasoulas is mentally fit to stand trial has told a Supreme Court judge it has been unable to reach a decision.

The jury of four women and eight men has been deliberating since 3:00pm on Monday after a special hearing lasting more than a week to determine whether he was mentally fit to stand trial on six counts of murder, 28 counts of attempted murder and other offences stemming from the tragedy in Melbourne's CBD last year.

Two psychiatrists told the jury Mr Gargasoulas, who has paranoid schizophrenia, is unfit to stand trial as his decision-making is based on his delusional beliefs.

Gargasoulas believes he is the 'second coming of Christ': psychiatrist

Mr Gargasoulas's lawyers have argued he should not stand trial because he is unable to enter a plea, instruct his lawyers, challenge jurors or understand the effect of the evidence against him.

Psychiatrist Lester Walton, who is engaged by the defence, told the jury Mr Gargasoulas was experiencing delusions including "specific beliefs that he is the messiah", the "second coming of Christ".

The court heard Mr Gargasoulas had signed a letter sent from prison as being from "the new king, King James George Gargasoulas ... king of kings, ruler of all the universe".

Dr Walton said Mr Gargasoulas told him that on the day of the Bourke Street tragedy he was on a mission to contact "Aboriginal royalty" who would initiate the process of recognising him as the messiah.

"He was being pursued by police and wanted to get rid of them in order to be free to pursue the promulgation of these ideas," he said.

But Michael Daffern, a psychologist engaged by the prosecution, told the court Mr Gargasoulas was fit to stand trial and understood the various pleas he could enter.

"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 told the hearing last week.

"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 Thomas Embling psychiatric hospital "visiting would be better … 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".

Gargasoulas 'wants to use trial as public platform': psychiatrist

His conclusion is at odds with another expert engaged by prosecutors — psychiatrist Andrew Carroll.

Dr Carroll gave evidence last week that Mr Gargasoulas was unfit to stand trial as his thinking is underpinned by his "messianic delusional belief that he is the saviour".

"Mr Gargasoulas is aware of the implications of a guilty plea … he absolutely wanted to make sure he had a trial of some kind so he has a public platform," Dr Carroll said.

"He understands the relevant facts … he can retain those facts, he can communicate his preferences to his lawyer.

"But where he falls down, in my view, is can he rationally weigh up the pros and cons of the pleas open to him?

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

On Tuesday, Justice Lex Lasry asked the jury to continue its deliberations for now in the hope it could reach a unanimous verdict.

If Mr Gargasoulas is found not to be fit for trial now, the prosecution can bring the case against him again within a year.