The man behind a deadly attack in central Melbourne was a terrorist and claims he was suffering from mental health issues are just a “lame excuse”, Prime Minister Scott Morrison says.

Somali-born Hassan Khalif Shire Ali, 30, fatally stabbed a well-known Melbourne restaurateur and injured two other people 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 Mr Morrison said that did not 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,” the Prime Minister told Network Ten on Monday.

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 who he had threatened with a knife. He later died in hospital.

But Shire Ali’s family said he had no 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.

Mr 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.

The front of Melbourne’s Pellegrini’s Espresso Bar was obscured by hundreds of floral tributes and messages of condolence on Monday.

There is barely a Melburnian who hasn’t dined or drunk a coffee at Pellegrini’s. Photo: AAP

The cafe was co-owned by popular 74-year-old restaurateur Sisto Malaspina, who was stabbed to death after going to help Shire Ali, witnesses say.

Mourners queued up at the cafe all weekend to pay their respects

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 on Monday.

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 on Monday.

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-AAP