Khayre was granted parole in December and was complying with his parole conditions until he killed a man, took a woman hostage and injured three police in a shootout on Monday.
According to media reports, the attacker was identified by police as an Australian national of the Chinese origin Yacqub Khayre, who had been allowed on parole after a trial over a massive terrorist suicide attack plot in 2010.
As Prime Minister Malcolm Turnbull put it, there are "very, very grave questions" to be answered over why this risky man was able to carry out this attack, which police are treating as an act of terrorism, in the name of Islamic State and al-Qaeda.
When he shot a man dead and took a woman hostage on Monday, he was out on parole after serving more than four years for assaulting a woman while robbing her house in an ice-fuelled attack.
Islamic State said via its news agency, Amaq, that the attack was launched because of Australia's membership in a USA -led coalition against the militant group.
Another man holding a woman against her will was found inside the building. "He had a long record of violence", Mr Turnbull told reporters.
Turnbull paid tribute to the swift response of police and offered condolences to the family of a man murdered in the attack at serviced apartments in the bayside suburb of Brighton.
Ashton said police were exploring whether radicalisation of Khayre had been exacerbated while he was in jail.
"There was something yelled", Mr Ashton said on Tuesday morning. Chief of staff Nicole Bland, who took the call, said she could hear a woman screaming in the background as the man declared "This is for IS".
"He was known to have connections, at least in the past, with violent extremism".
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He was charged and acquitted over a foiled plot to attack the Holsworthy Army barracks in Sydney in 2009.
'We certainly want to make sure that people like Khayre are not released on parole and we are going to have a very serious discussion about this at COAG, ' he told 3AW on Wednesday.
Ashton said he believed the gunman was acting alone.
One police officer was shot in the neck and ear and two officers suffered wounds to their hands, but none of the wounds was life-threatening, Mr Ashton said.
Dr Nicola McGarrity, who represented one of the men convicted over the 2009 Holsworthy terror plot, told The New Daily that parole serves an important goal in the criminal justice system.
Mr Andrews also said he would give police more powers if needed after the Brighton terrorist attack.
Comm Ashton said he had been on parole since being released from prison last November and "there was nothing wrong with his parole until yesterday".
Crisp said police had not confirmed the identity of the gunman, and he would not elaborate on the phone call to Seven.
"There is no place in Australia for such cowardly violence", the Somali Australian Council of Australia said in a statement.