Australia's prime minister on Tuesday suggested a visiting Frenchman who heroically fended off a knife-wielding Sydney mall attacker using only a bollard could be offered citizenship.

Damien Guerot has been dubbed "bollard man" and a "hero" of Saturday's attack that killed six people and wounded a dozen more.

Prime Minister Anthony Albanese singled Guerot out for praise on Tuesday, thanking him for his "extraordinary bravery" in confronting Joel Cauchi on an escalator and preventing the 40-year-old attacker from reaching more victims.

"I say this to Damien Guerot who is dealing with his visa applications, that you are welcome here, you are welcome to stay for as long as you like," Albanese said.

"This is someone who we would welcome becoming an Australian citizen, although that would of course be a loss for France. We thank him for his extraordinary bravery."

"It says a lot about the nature of humanity at a time when we are facing difficult issues, that someone who is not a citizen of this country stood bravely at the top of those escalators and stopped this perpetrator from getting onto another floor and potentially inflicting further carnage on citizens," Albanese said.

Australians have been shocked by the Saturday attack that took place in a busy shopping mall in the city's eastern suburbs.

Five women and one Pakistani security guard were killed during the rampage, which has not been blamed on terrorism.

Police are investigating whether Cauchi, who had a history of mental illness, targeted women specifically.

But Australians and Albanese took some succour from strangers aiding each other during the attack and from the bravery of policewoman Amy Scott, who acting alone, tracked Cauchi down and shot him dead.

"I think that on Saturday we saw some of the best of human character at the same time as we saw such devastating tragedy," Albanese said.