The man shot dead by gunman Yacqub Khayre in a Melbourne serviced apartment complex on Monday has been named as Kai Hao.
He forced her to call Channel Seven news in Melbourne during the stand-off with police, then said: "This is for IS (Islamic State)".
The Islamic State group claimed responsibility for the siege, in which a man was killed, several police were injured and a woman was held against her will.
The group has claimed responsibility for a wave of deadly incidents in the United Kingdom, including the weekend attack in London that left seven people dead and nearly 50 injured. Prime Minister Malcolm Turnbull described yesterday's incident in the southeastern suburb of Brighton as a "terrorist attack" that underlined the need for constant vigilance in the face of Islamist extremism. He was recognised as a refugee under Australia's humanitarian migration program and later became an Australian citizen, police said.
But it was too early to know if the terrorist set out to target police or "seized the opportunity he thought was presented to him last evening", Ashton said.
"This terrorist attack by a known criminal, a man who was only recently released on parole, is a shocking, cowardly crime".
Australia is a key ally of the USA and is flying combat missions against Islamic State in Syria.
ISIS issued the claim through its Amaq News Agency in Arabic and English.
The siege came to a dramatic end when the gunman opened fire on police, hitting three male police officers, two of whom were hospitalised with gunshot wounds while the other was treated at the scene.
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"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.
Khayre was released on parole late a year ago after serving time for intent to cause injury and arson, which Turnbull said was a concern given his background and something that would be reviewed.
The Australian authorities are treating an abduction and a killing near Melbourne on Monday, which ended with the gunman dead, as a terrorist attack.
In 2009, he was acquitted of a plot to attack an Australian army base in Sydney.
Australian officials say they have prevented 12 attacks in the country since the threat level was raised from "possible" to "probable" in September 2014.
Three special operations officers were shot in the siege, in Melbourne's affluent suburb of Brighton.
Three police officers also sustained non-life threatening injuries during the siege.
Ashton also downplayed any link to the recent Manchester and London terror attacks.
"We asked for more information and that's when he hung up", Pristel added.
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