Remember the man and the smile, not the violence of his death.

That's the message from Prime Minister Scott Morrison, who has visited a Melbourne cafe co-owned by Sisto Malaspina, killed in a city street terror attack.

Pellegrini's Espresso Bar on Tuesday reopened its doors, offering its famous coffee to a bumper crowd, which included Mr Morrison.

"The stories of his passion are just overwhelming," the prime minister told reporters of Mr Malaspina.

"(These people) are celebrating a life well lived despite how violently and terribly it was taken. And it is the hope of his life that completely transcends the evilness of how it was taken from him and from us."

The 74-year-old was killed and two other men were injured on Friday when when 30-year-old Hassan Khalif Shire Ali drove a burning ute into the city and launched a knife attack.

Police shot the knife man who later died in hospital.

Mr Morrison again thanked police and other emergency service personnel who responded to Friday's attack and he asked that Mr Malaspina be remembered as a much-loved character.

"The Sisto smile is the best thing to project back to those who would seek to take that smile from us," the prime minister said.

"The best way we can honour him is to love life and to love each other."

When the cafe's doors opened at 8am there was already a line-up.

The iconic restaurant is offering free long blacks, Mr Malaspina's coffee of choice, to customers throughout Tuesday.

"It's been a good experience, a strange experience. I see today as the beginning of the celebration of Sisto's life. You can only cry so much," his nephew Rob Cecchini told AAP on Tuesday.

"I'm sure he would have wanted us all to do just that - celebrate his life."

Mr Cecchini said seeing his uncle's empty stool was difficult but he was trying to "push through".

The family has accepted the offer of a state funeral Premier Daniel Andrews on Tuesday confirmed the service would be held next Tuesday at East Melbourne's St Patrick's Cathedral.

Federal Opposition Leader Bill Shorten called for calm in the aftermath of the Melbourne attack.

"I can understand why people want to lash out, want to blame different groups or want to blame politicians or want to blame Mr Morrison, I actually think we've got to take a step back," he told reporters in Melbourne.

"Now is the time to work out what we can all do better. For me it's not about one group or politician, what can we all do better to keep Australians safe."

Mr Malaspina had co-owned Pellegrini's since 1974 and the man with a "flamboyant personality" and venue became Melbourne icons.