The woman taken hostage was rescued from the apartment and "is safe and well" with investigators, police said.
Yacqub Khayre, the 29-year-old gunman who killed a man, took a woman hostage and sparked a siege in Melbourne yesterday, was not on the radar of counter-terror police after his release from prison in December 2016, the ABC has learned.
"What is clear here is that we face a growing threat from Islamist terrorism in Australia, in our region and around the world".
"Subsequently he (Khayre) came out of the apartment with a shotgun and commenced to fire at police at the entryway to the apartments", Ashton said.
Police discovered the body of a man with gunshot wounds in the foyer.
A gunman behind a deadly terrorist siege that claimed the life of an innocent apartment clerk in Melbourne, Australia had been acquitted of plotting to attack an Australian army base and served time for a string of violent offences.
The Age reported that the unnamed woman taken hostage - aged in her 20s or 30s - was also an employee at the serviced apartments. He was shot and killed approximately 20 minutes later by special operations police forces after an exchange of gunfire outside the building, during which three police received minor injuries.
A news outlet for the group said it had carried out the attack.
'We'll look at that very closely, of course, and if there are any changes in any element of this act - which we're considering as an act of terror - then we stand ready to make them, ' Mr Andrews said of changes to parole.More news: Britain's opposition leader calls on May to quit over police cuts
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The Islamic State claimed responsibility for the attack early Tuesday morning, Melbourne time (Monday afternoon Eastern time), calling the assailant a "soldier" of the terrorist group. "It is a terrorist attack and it underlines the need for us to be constantly vigilant", he said.
Mr Ashton said there was nothing to indicate the man was planning an attack and said police were now trying to establish his motivation.
He had "a long criminal history" and was on parole after being released from jail on a separate offence past year, Mr Ashton said.
The evidence pointing to terrorism first emerged with a call to a television station during the siege, in which a man said, "This is for IS", presumably a reference to the Islamic State, and, "This is for al-Qaeda".
He said Khayre had been acquitted over a foiled plot to attack a Sydney army barracks in 2009.
"He appears to (have been) in the wrong place at the wrong time", Mr Ashton said. A teenager killed a Sydney police officer in October 2015 in what was considered a "politically motivated" attack.
Victorian Premier Daniel Andrews said had been compliant with his parole conditions.
"This person wasn't someone around which we had major concerns at this time, and we had nothing to suggest (he was planning) what he did suddenly decide to do".
"He is someone that was known to us as having a long criminal history, a whole range of offending going back many years ago".