Police shot dead the gunman, Yacqub Khayre, who they said had a long criminal history, on Monday after he killed a man in the foyer of an apartment block in Melbourne, Australia's second-largest city, and held a woman hostage inside.
Senior officials confirmed that Khayre had been acquitted of a plot to attack a Sydney army base in 2009 and was on parole for a violent home invasion at the time of Monday's siege.
"This terrorist attack by a known criminal, a man who was only recently released on parole, is a shocking, cowardly crime," Prime Minister Malcolm Turnbull told reporters in the capital, Canberra.
"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.
Police also said they were investigating the siege as act of terrorism after ISIS claimed responsibility for the attack via its Amaq news agency. They identified Khayre as a 29-year-old Australian of Somali heritage.
Amaq said the attack was launched because of Australia's membership of a U.S.-led coalition fighting against the terrorists in Syria and Iraq.
Police said they were investigating whether Khayre had any established links with the group.
Victoria state Police Commissioner Graham Ashton said earlier Khayre had arranged to meet a female escort at a block of serviced apartments in the beachside Melbourne suburb of Brighton on Monday.
After shooting and killing a staff member when he arrived, Khayre then held the woman hostage for several hours before he burst out of the building and engaged police in a firefight, during which he was killed.
The woman was unhurt but three police officers suffered gunshot wounds that were not life-threatening, Ashton said.
Police are investigating whether Khayre tried to lure police into an ambush. Australia has not increased its terror threat level and police said they were not looking for any other suspects.
A spokeswoman for Vixen Collective, an oganisation representing sex workers, said she did not believe escorts were specifically targeted given ISIS had recently encouraged readers of its magazine to lure people via various means, including fake classified ads.
Turnbull questioned why Khayre was not behind bars after a string of offences.
The Victorian Supreme Court was told during that case that Khayre had been a worshipper at a Melbourne mosque and at a nearby prayer hall regarded by police as an "incubator" of extremist ideology.
Prosecutors unsuccessfully argued that Khayre travelled to Somalia to obtain a fatwa, or religious ruling, in support of the Sydney plot.
Court documents show Khayre migrated as a child with his family to Australia through a Kenyan refugee camp. He was recognised as a refugee under Australia's humanitarian migration programme and later became a citizen, police said.
"There is no place in Australia for such cowardly violence," the Somali Australian Council of Australia said in a statement.
Forensic investigators were at Khayre's family home in Melbourne's suburban Roxborough Park, according to a Reuters witness. Police said they were also conducting "reassurance patrols" to calm the neighbourhood.
He was jailed in 2012 over a violent burglary in Melbourne, where he was found to have repeatedly struck a woman and her father. Khayre was given a five-and-a-half year prison term, according to court documents. He was granted parole in December.
Tightening of parole conditions is now likely to form a centrepiece of the next meeting between Turnbull and the state government leaders on Friday.
SIEGE SPARKS IMMIGRATION DEBATE
Australia, a staunch ally of the United States, has been on heightened alert for attacks by home-grown terrorists returning from fighting in the Middle East, or their supporters, since 2014.
In December 2014, a gunman killed one hostage during a 17-hour siege at a popular Sydney cafe. Another hostage was killed by fragments of a bullet fired by police who stormed the cafe and killed the gunman.
The Melbourne siege has sparked debate about immigration and travel policies. Far-right leader Pauline Hanson said she would support a travel ban like the one U.S. President Donald Trump is trying to introduce.
"(Turnbull should) look seriously at instituting a moratorium on immigration of Muslims to Australia or, at the very least, greater stringency in vetting those wishing to come to our country," said Hanson.
(Additional reporting by Tom Westbrook, Jonathan Barrett and Colin Packham in SYDNEY; Writing by Jane Wardell; Editing by Paul Tait, Robert Birsel)