A man who was killed by a gunman in a Melbourne siege being investigated as a terrorism incident has been identified.

PM Malcolm Turnbull named the victim as Kai Hao. He was a 36-year-old newly married father, local media said.

The gunman, Yacqub Khayre, also injured three police officers and took a woman hostage during the siege at an apartment building on Monday night.

Khayre, 29, was shot dead by police after confronting them with a sawn-off shotgun.

The hostage, a 36-year-old woman, was not physically harmed, authorities said.

Police were investigating whether Khayre, a Somali-born Australian citizen, may have lured officers to the wealthy suburb of Brighton with the aim of ambushing them.

Victoria Police Chief Commissioner Graham Ashton said Mr Hao was a building employee and “in the wrong place at the wrong time”.

Parole changes signalled

Mr Ashton confirmed police had begun a terrorism investigation after Khayre made comments referencing so-called Islamic State and al-Qaeda.

The siege has ignited debate about local parole laws after it emerged Khayre had a history of violence and was released from jail last year following an aggravated burglary.

In 2009, he was acquitted over a foiled plot to attack a Sydney army barracks.

The Australian government has said it will debate toughening parole laws later this week.

“I think the public are entitled to expect that people who present that level of danger to the public, and who have a terrorism background, there should be a presumption against bail or parole except in a very clear case,” Attorney-General George Brandis told the ABC.

However, the chairman of the Adult Parole Board said it was not informed Khayre was on a terror watch list.

“We had been told nothing about him that would indicate any suggestion of risk,” Peter Couzens told Macquarie Radio.

“Had we been told, we would have acted.”

Last month, an Australian coroner criticised a decision which allowed bail to a gunman behind Sydney’s deadly cafe siege in 2014.