Bourke Street killer Hassan Khalif Shire Ali, 30, had been interviewed by ASIO and banned from leaving the country, but had no “definite link” to the Islamic State terror group, Home Affairs Minister Peter Dutton said.

“There’s not, as I’m advised, a membership of an organisation or a definite link to ISIL,” Mr Dutton told journalists in Brisbane on Sunday.

“It’s more – at least the working theory is at the moment – a case where this person has been downloading information or receiving information, messages in his own mind about what he should be doing.”

The press conference marked the first serious attempt by authorities to explain how Shire Ali was able to plan and carry out Friday’s attack while he was known to intelligence agencies.

“The judgment that was made about this individual was that he was not in the planning stage of an attack,” Mr Dutton said.

“Where you’ve got somebody who picks up a kitchen knife and grabs a couple of gas bottles and drives into the CBD, these are very difficult circumstances to stop.”

Shire Ali had his passport cancelled in 2015, and Mr Dutton confirmed that travel ban was still in place at the time of the attack.

Mourners queued up at Pelligrini’s Espresso Bar over the weekend to pay respects for co-owner Sisto Malaspina. Photo: AAP

Victorian Police Chief Commissioner Graham Ashton on Saturday said Shire Ali’s attack – stabbing three civilians, one fatally, and setting a car on fire – was terrorism inspired by Islamic State.

Police said the Somalia-born man, 30, had planned to cause an explosion.

He was shot in the chest by a police officer and died in hospital.

The Islamic State terror group swiftly claimed responsibility for the knife attack, although it provided no proof to support its claim.

“The one who executed the ramming and stabbing operation in Melbourne … is one of the fighters of the Islamic State and he executed the operation in response to [a call] to target the citizens of the coalition,” the terror group posted online on Friday.

Mr Dutton said the Australian public needed to be “realistic about the threat”, as there are currently “400-plus people under investigation” in relation to potential terrorism.

“We’ve been able to stop 14 [terror attacks]. Seven have got through, tragically, and our job is to make sure the eighth doesn’t happen,” Mr Dutton said.

The family of the attacker said he had mental health problems.

“Hassan suffered from mental illness for years and refused help. He’s been deteriorating these past few months,” a note given to Nine News showed.

“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.”

Victorian Premier Daniel Andrews said the “act of evil” was not enough to change the heart of the city.

“We will do, and have done everything possible, to keep Victorians safe from an infrastructure point of view. But we are not going to fundamentally change the way the city works, for instance, running trams,” Mr Andrews said on Sunday.

He stopped short of calling for drastic safety measures, preferring a “proportionate response to a very real threat”.

On Sunday, thousands of Melburnians gathered to mourn the victim of Friday’s alleged terror attack on Bourke Street, and to commemorate the 100-year anniversary of the end of World War I, despite the recent attack and heightened security.

Sisto Malaspina was an integral part of Melbourne’s restaurant scene. Photo: Twitter

More people than expected attended the ceremony at the Shrine of Remembrance, keen to show they were not bowed.

Premier Daniel Andrews praised Victorians for flocking in their thousands to the Shrine of Remembrance in defiance of Friday’s act of “pure evil”. He had earlier described the incident as “an act of terror”.

Melbourne’s Pellegrini’s Espresso Bar, obscured by hundreds of floral tributes and messages of condolence, remained closed on Sunday.

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.

Mr Andrews spoke to Mr Malaspina’s family on Sunday afternoon and offered a state funeral. The family have not made a decision as of Sunday evening.

The spot on Bourke Street where Sisto was fatally stabbed has also been turned into a makeshift shrine.

There was a heightened police presence across the CBD at sporting events and other gatherings across Melbourne over the weekend, including the Flemington races, soccer and Remembrance Day ceremonies. But this did not deter the crowds.

The iconic Bourke Street mall was reopened on Saturday. The street, a popular shopping strip, buzzed with pedestrians over the weekend, despite the recent horror.

A brave passerby dubbed the ‘trolley man’ ­– for ramming the attacker with a trolley to help police ­– has been named as 46-year-old Michael Rogers.

Michael Rogers was dubbed ‘trolley man’ after ramming the attacker with a trolley to help police. Photo: Seven News

He is currently homeless and his phone was destroyed in the incident on Friday, according to the National Homeless Collective.

The charity had crowdfunded more than $60,000 from grateful Melburnians by Sunday evening, which will be handed over to Mr Rogers on Monday.

“I threw the trolley straight at him, and I got him. I didn’t quite get him down, though. I’m no hero,” Mr Rogers told Seven News.

Tasmanian businessman Rod Patterson and a 24-year-old security guard were also injured in the attack.

Mr Patterson said he was injured while trying to help others caught up in the attack on Friday.

“Whilst out with my wife Maree enjoying another great day in Melbourne, a city that we love, we were unfortunately caught up in the incident on Bourke Street,” he said in a statement on Saturday.

“I went to assist and whilst doing so received a knife wound to my head.”

-with AAP

Rod Patterson was injured while trying to help others caught up in the stabbing. Photo: AAP