Hassan Khalif Shire Ali, 30, fatally stabbed one man and injured two others after fire-bombing his car in Bourke Street on Friday.
Shire Ali’s family have since said he had been experiencing mental health issues for years, had refused help and was deteriorating.
But Morrison says this doesn’t change the “facts”.
“He was a terrorist. He was a radical, extremist, terrorist, who took a knife to another Australian because he had been radicalised in this country, and we can’t give him excuses,” he told Network Ten today.
“These other issues are relevant. Don’t get me wrong, but he was radicalised, and that’s why he took a knife to people.”
Shire Ali was known to federal police and had his passport cancelled in 2015 amid concerns he planned to travel to Syria to fight with Islamic State.
The Somalia-born man was shot in the chest by a police officer after threatened him with the knife and later died in hospital.
But his family said he didn’t have terrorist connections.
“Please stop turning this into a political game. This isn’t a guy who had any connections with terrorism but was simply crying for help,” they said in a note handed to reporters.
Morrison again called out the “vile evil” of radicalisation and urged Muslim community leaders to call it out.
“There is, I think, a very positive level of cooperation but there needs to be a heightened sense because you can’t watch everybody,” he said.
Home Affairs Minister Peter Dutton is open to suggestions to improve Australia’s response to terrorist threats but also stressed the help of the Muslim community was key.
“We need the community, particularly leaders within the Islamic community, to do even more to encourage people to alert authorities, to change behaviour. That might give us a tip-off to stop the sort of behaviour we saw last week,” he told Seven Network today.
Labor spokeswoman Michelle Rowland highlighted the role all Australians can play in fighting extremism.
“Everyone in the parliament is united in ensuring that the first responsibility of us as public office holders is to keep Australians safe and ensure we do everything in our power in order to make that happen,” she told Sky News today.
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