Australian police are treating a shooting and hostage situation in Melbourne that left two men dead, including the attacker, as an "act of terrorism". It comes after Islamic State reportedly claimed responsibility for the drama.

"We are treating it as an act of terrorism," Victoria state police Commissioner Graham Ashton said on Tuesday.

"We believe this person was there with those sorts of [terrorist] intentions, albeit we don't know whether it was something planned or something spontaneous at this stage," he said.

Authorities have identified the attacker as a Somali-born man, Yacqub Khayre, 29, who lived with his mother in a Melbourne suburb. Police are now searching the mother's house.

Khayre was on parole after serving time in prison for a violent burglary in 2012, Ashton said. According to Australian media, he was also known to counter-terrorism authorities for his alleged involvement in a 2009 terror plot to attack the army barracks in Sydney.

Victoria police shot dead the man involved in the hostage situation at an apartment in Brighton near Melbourne Monday, after he began firing on police just before 6pm local time.

The Amaq news agency, which is affiliated with IS, said the shooting was carried out by a "soldier" of their terrorist organization, according to Reuters.

While police are treating the incident as an act of terrorism, Ashton was not able to confirm that ISIS was behind the attack.

"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, alleging that maybe he subscribed to Al-Qaeda ideology.

Ashton added that so far there was "no evidence" to suggest that the attack was linked to recent terror attacks in Manchester and London.