Australian Prime Minister Malcolm Turnbull said on Tuesday police were treating a deadly siege in the southern city of Melbourne as an "act of terrorism" after a claim by the Islamic State group that one of its fighters was the gunman responsible, Reuters reported.
Police shot dead gunman Yacqub Khayre on Monday after he held a woman hostage inside an apartment building in Melbourne, Australia's second-largest city.
Police confirmed on Tuesday that Khayre, who was acquitted of a plot to attack a Sydney army base in 2009, had shot a man dead in the foyer of the building.
"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.
Victoria state Police Commissioner Graham Ashton said police were still investigating after Islamic State claimed responsibility for the attack via its Amaq news agency.
"We're aware of them having claimed responsibility, but then they always tend to jump up and claim responsibility every time something happens so we note that that has happened," he said.
Amaq said the attack was launched because of Australia's membership in a U.S.-led coalition fighting against the militant Islamist group in Syria and Iraq.
Police were also investigating a telephone call made to the newsroom of Australian TV broadcaster Seven Network during the siege. Seven reported that a male caller said the attack was related to Islamic State.
Ashton said Khayre, an 29-year-old Australian of Somali heritage, had a long criminal history and was on parole at the time of the attack.
He did not specify the charges related to Khayre's parole. Khayre was acquitted of a plot to attack Sydney's Holsworthy Barracks in 2009. Three other men were convicted.
Ashton said evidence collected from a raid on the home that Khayre lived in with his mother indicated he likely acted alone and that the threat from this attack was now over.
Khayre arranged to meet a female escort at a block of serviced apartments in the beachside Melbourne suburb of Brighton on Monday, and then killed a staff member when he arrived, Ashton said.
After holding the woman hostage for several hours, Khayre burst out of the building firing at police, who shot back and killed him. The woman was rescued unhurt, but three police officers suffered non-life threatening gunshot wounds.
Australia, a staunch ally of the United States, has been on heightened alert for attacks by home-grown militants returning from fighting in the Middle East, or their supporters, since 2014. Police have foiled several major plots in recent years.
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, who was not affiliated to any militant groups and acted alone.
Six people were arrested over a plan to set off bombs in Melbourne on Christmas Day last year.