Prosecutors are calling for the 42-year-old to be given a life sentence without the prospect of parole, seven years after he fatally stabbed Kylie Blackwood and left Ilona Prohaska for dead.

Given Murdoch pleaded guilty it is an unusual request, Nick Papas QC conceded in a pre-sentence hearing at Victoria's Supreme Court.

But Murdoch has demonstrated a "disturbing pattern of behaviour" in past crimes and has shown no remorse, he told Justice Jane Dixon.

The 2013 attacks on Ms Blackwood and Ms Prohaska occurred while Murdoch was on parole for an earlier attack on a woman in her own home.

That woman was struck over the head and stabbed in the neck, causing life-threatening injuries and brain damage.

"There is a chilling similarity," Mr Papas said.

Murdoch's behaviour following the latest attacks was also "extraordinarily cold", he said.

Leaving Ms Prohaska unconscious and bleeding significantly in May 2013, Murdoch took money from her bank account and went to a meeting with Corrections Victoria.

After killing Ms Blackwood three months later, Murdoch tried three times to use her ATM card and appeared "almost removed from any sense of what had happened".

Ms Blackwood saw her husband and children off to work and school on the morning of August 1, 2013, spoke to a friend on the phone and went shopping.

Disturbances in the house tell a story of a confrontation by Murdoch that led from the study to the sunroom, where Ms Blackwood was repeatedly stabbed in the neck and chest, Mr Papas said.

That day is one Peter Blackwood says he will never forget or forgive.

His wife was a doting mother and a tenacious and spirited woman. "She would have went down fighting," he said.

Her body was discovered by her then-11-year-old twins Mia and Holly, who are haunted by the memories of what they saw that day.

"It's unfair and it's heartbreaking," Mia, now 17, wrote to Victoria's Supreme Court.

"Everywhere I go I feel empty .. after doing something like that, how can you call yourself a human being," Holly added.

Their older brother Chase asked that Justice Dixon "please bring justice to my family".

Ms Prohaska, now 80, watched by video link and told the court she lost the will to live after the attack.

Murdoch had broken into her Endeavour Hills home, knocking the then 73-year-old to the ground and cutting her throat.

He took $70 and a debit card from her, forced her down a flight of stairs and hammered a knife into each side of her neck, causing significant blood loss.

Murdoch's lawyer Jim Shaw agreed a life sentence would not be inappropriate, but said he would argue Murdoch should be given the prospect of parole.

The pre-sentence hearing will continue on March 4.

Australian Associated Press