Australian Prime Minister Malcolm Turnbull on Tuesday termed the Melbourne hostage crisis as a "terrorist incident", as police launched a probe into the attack claimed by the Islamic State that left two men dead and three officers injured.

Turnbull said there was no evidence to suggest that the last night's attack was a coordinated attack and that others were involved in planning and carrying out the assault.

"This terrorist attack by a known criminal, a man who was only recently released on parole, is a shocking, cowardly crime. It is a terrorist attack and it underlines the need for us to be constantly vigilant, never to be deterred, always defiant, in the face of Islamist terrorism," he said.

"What is clear here is that we face a growing threat from Islamist terrorism in Australia, in our region and around the world. We will continue to defy it and we will continue to defeat it." 

Turnbull confirmed that the dead gunman, Yacqub Khayre, had been previously acquitted of terror-related charges, and said there were "grave questions" about why he was out on parole despite a known record of violent offending.

"I have raised these with the Victorian Premier, whom I called last night and I called again this morning. How was this man on parole? He had a long record of violence…He had been charged with a terrorist offence some years ago and had been acquitted," he said.

"Now, there is an investigation going on at the moment.

There is a lot about this incident that is not known. But we do know it was a terrorist attack and he has claimed, the offender claimed that quite specifically," Turnbull said.

Meanwhile, the bomb disposal squad and forensics police today searched the scene of the siege in Brighton suburb of Melbourne while officers were raiding the home of the gunman who killed one man yesterday.

Local media reports said that police carried paper bags of evidence containing a book with Arabic writing from Buckingham Serviced Apartments on Bay Street, where Khayre held a sex worker hostage before he was killed by police.

Khayre had been on parole since late last year and had a long record of serious criminal offending including offences for drugs, firearms and violence and was being investigated for possible links to terrorism.

He was acquitted in a 2009 terror plot to kill military personnel at Holsworthy army barracks in Sydney.

Police believe he became radicalised after attending Preston mosque with other men who were also charged over the barracks plot.

Khayre was later jailed for five years and six months for a violent home invasion in 2013.

Victoria Police Chief Commissioner Graham Ashton said the incident was being treated as "an act of terrorism".

Police said they believe that Khayre was acting alone and have released a statement encouraging Victorians to go about their daily business, saying there is no current threat.

"Nothing we have found thus far suggests to us this was anything that was planned or done in concert with others," he said. "We believe at this stage he was acting alone and there is no ongoing threat in relation to a plot." 

Islamic State's Amaq propaganda news agency today claimed responsibility for the attack.

A review into the Khayre's prison and parole management has been ordered.

Khayre shot dead a China-born clerk working at an apartment building yesterday and took a female escort hostage.

He was shot dead following a stand-off with police.