Australia has invited a French national who confronted a knife-wielding attacker during a rampage in a Sydney mall to stay in the country permanently, heeding calls from the public who had hailed him a hero who deserved citizenship.

A video of Damien Guerot, a construction worker, confronting the assailant Joel Cauchi with a bollard during Saturday's attack in Sydney went viral on social media.

Six people were killed and 12 wounded in the attack at the beachside mall, one of the city's worst violent crimes in recent years. Cauchi, who police said appeared to have been targeting women, was shot and killed by Inspector Amy Scott, who confronted him solo during his rampage.

As the city mourned the victims and cheered the heroes who emerged from the incident, there were growing calls to give Guerot, whose visa expires in a month, the right to remain in the country.

Prime Minister Anthony Albanese said Guerot was welcome to stay.

"You're welcome to stay for as long as you like," Albanese told a press conference, in reply to a question about his heroics.

"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," he said.

Reuters could not reach Guerot for a response to the Prime Minister's comments.

Viral videos circulating on social media show Guerot, wearing a white t-shirt and black trousers, standing at the top of an escalator holding up a bollard and trying to throw it at Cauchi.

Albanese said his act prevented the perpetrator from getting on to another floor and potentially inflicting further carnage.

Another video showed him chasing behind Inspector Amy Scott, who shot the attacker dead, holding a chair as a potential weapon.

Guerot who spoke to Channel Seven earlier this week said he was on his way to the gym when the attack started. He and his friend, Silas Despreaux, were just acting on adrenaline, he said.

"I don't know, we just (thought) we need to do something to catch him," Guerot said. "You cannot think in that moment, it's adrenaline."

His heroics was quickly followed by an online petition calling for Guerot to be granted Australia citizenship, describing his actions as "a true act of Australianism" that saved lives.

In a social media post, French President Emmanuel Macron hailed Guerot and Despreaux as "true heroes" for their actions during the Sydney mall attack.

"Very great pride and recognition," he said on X.