Melbourne 'terrorist' who killed a man and held hostage an escort was a long-time criminal.

A long-time criminal is the terrorist behind the deadly Brighton siege that claimed the life of an innocent apartment clerk.

The Somalian-born man, 29, had served jail time over a violent burglary in 2012 and was on parole at the time of Monday’s siege, Chief Commissioner Graham Ashton said.

Mr Ashton said he had been on parole since being released from prison last November and “there was nothing wrong with his parole until yesterday.”

The man – who we will not be naming – also spent 16 months on remand before being acquitted of the 2009 Holsworthy army barracks terror plot in Sydney.

He lived in the Melbourne suburb Roxburgh Park with his mother and police will search their home on Tuesday, as well as continue work at the Bay St serviced apartment block.

Islamic State has claimed responsibility for Monday’s incident, but Mr Ashton downplayed their statement.

“We’re aware of, online, them having claimed responsibility, but then they always tend to jump up and claim responsibility every time something happens,” he told reporters.

“… But he’s also made statements last night around (rival organisation) al-Qaeda.”

Police shot dead the man as he stormed out of the Bay St, Brighton serviced apartment building shortly before 6pm and began firing.

Two officers – including one with wounds to his face and neck – were taken to hospital while a third was treated at the scene.

A female escort held hostage was rescued from the ground floor apartment.

Officers had earlier found the body of a clerk, an Australian national born in China, in the foyer.

“He appears to (have been) in the wrong place at the wrong time,” Mr Ashton said.

He said it was too early to know what the man had been planning, but said it was a “possibility” that he wanted to ambush police.

“That’s all been weighed into the calculations but we haven’t found anything like a note or anything like that so far.”