Police conducted raids at two homes in the city's western suburbs on Saturday, the day after Hassan Khalif Shire Ali drove a 4x4 vehicle loaded with gas bottles into the city centre, ignited the vehicle into a ball of flames, and then stabbed three people.
Police said Shire Ali's Australian passport was cancelled in 2015 after an intelligence report he planned to travel to Syria, but an assessment was made that while he had radical views, he posed no threat to national security.
The cylinders did not explode and the fire was put out in 10 minutes, by which point the attack was over, though not before one man was fatally stabbed.
"It looks like he's attempted to ignite a fire in the vehicle, we believe at this stage with a view to igniting those canisters with some sort of explosion, but that didn't eventuate", Ashton told reporters.
According to media reports, the IS had claimed responsibility for the attack via the Amaq news agency, which said the man was "one of Islamic State fighters" and had responded to IS calls for attacks in countries that are part of the global coalition fighting the militants in Syria and Iraq. He had a criminal history for cannabis use, theft and driving offences, Ashton said.
First responders work the scene of the fatal stabbing in Melbourne on November 9, 2018.
"The event yesterday for us is a reality check, even with the fall of the (Isis) caliphate. the threat continues to be real", the acting deputy commissioner for national security, Ian McCartney, said.
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"We're not saying there was direct contact".
The prime minister, Scott Morrison, on Saturday blamed the attack on religious extremism. "I am the first to protect religious freedom in this country, but that also means I must be the first to call out religious extremism", he said. "We're saying it was more from an inspirational perspective", McCartney said.
Morrison said he had long-standing relationships with the Muslim community and it was them who had raised with him concerns about radicalism in recent years. One note read "you always looked after us like family".
They did not, however, offer any evidence for the claim. It said the man was an ISIS fighter and had responded to the group's calls for attacks in countries that are part of the global coalition fighting the militants in Syria and Iraq.
Mr Shire Ali was killed at the scene when he was shot by police officers after lunging at them with a knife.
Victoria state police said counter-terrorism investigators were searching two properties in suburban Melbourne in connection with the attack, but there was no immediate word on what the searches yielded. A 26-year-old man was in a stable condition in the Royal Melbourne Hospital, while a 58-year-old also remains in hospital with non-life threatening injuries. It's the second time in four years Australia has witnessed militant violence.
Two hostages were killed during the 17-hour Sydney cafe siege by a "lone wolf" gunman who was inspired by Islamic State militants. "From what we know of that individual, we are treating this as a terrorism incident", he said of the attacker.