The gunman identified as Yacqub Khayre was shot dead yesterday following a stand-off with police which lasted for more than an hour at serviced apartments on Bay Street in Brighton, 11km south-east of Melbourne's central business district.
Victoria Police Chief Commissioner Graham Ashton said Khayre, was known to police and had a long criminal history.
Khayre was charged and acquitted by a jury over a plot to attack the Holsworthy Army barracks in Sydney in 2009.
Ashton was quoted as saying by the ABC that the siege was being treated as a "terrorism incident".
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"He has a long criminal history with us, but also from what we're piecing together comments he made related to Islamic State and Al-Qaeda certainly for us put this in the terrorism category," he said, adding that, Khayre was released on parole in November last year.
"He has recently done some jail time, he got out late last year and has been on parole at the time of this offending last night," he said.
ABC had reported that the Islamic state claimed responsibility for the siege through a published statement via Amaq news agency which is affiliated to the terror group.
It said the attack in Melbourne was carried out by one of its "soldiers".
"The attack in Melbourne, Australia was carried out by a soldier of the Islamic State in response to the call for targeting the subjects of the coalition states," the statement said.
"That's all part of the investigation at this point in time as to who made that phone call, but we will certainly be working with Channel 7 in relation to that phone call," he said.
The siege began after emergency services responded to reports of an explosion at the apartment building at 4pm in the evening.
Police discovered the body of a man with gunshot wounds in the foyer.
Dozens of gunshots rang out just after 6 PM in Bay Street with crowds of people fleeing and taking refuge in a nearby supermarket.
Three police officers were shot by the gunman during the shoot-out. A woman, in her 20s who was held hostage by Khayre was rescued.