A man went on a stabbing rampage in downtown Sydney, Australia, on Tuesday, killing one woman and wounding another before he was restrained by members of the public, police said.

The man has a history of mental illness and is suspected of attempting to stab other people while yelling "Allahu akbar," or "God is great," police and witnesses said.

Police have not labelled the rampage an act of terrorism, although the 21-year-old, who was not named by police, had collected information on his computer about mass killings in North America and New Zealand, New South Wales state Police Commissioner Michael Fuller said.

"It is not currently classed as a terrorist incident. Obviously as the investigation continues we will reassess that," Fuller told reporters.

"He is by definition, at the moment, a lone actor. Information was found on him that would suggest he has some ideologies in relation to terrorism, but he has no links to terrorism," Fuller said. "There was certainly information found on him about other crimes of mass casualties and mass deaths around the world."

Watch as members of the public restrain knife-wielding man:

Several pedestrians got creative with materials on hand to restrain suspect in a fatal stabbing in Sydney, Australia. 1:30

A gunman who recently killed 22 people at a Texas Walmart appears to have praised the March 15 shootings in Christchurch, New Zealand, where an Australian white supremacist is charged with killing 51 worshippers at two mosques.

Witnesses said the assailant Tuesday was carrying a 30-centimetre knife and attempted to stab multiple people near a busy intersection in Australia's largest city at around 2 p.m. Fuller described the weapon as a butcher's knife.

Police said a man was arrested, and a 41-year-old woman with a stab wound to her back was taken to a hospital in stable condition.

Police said the body of a 21-year-old woman was later discovered in a nearby fourth-floor apartment.

Bystanders used chairs and milk crate to restrain stabber

"A number of members of the public physically restrained the offender," police Supt. Gavin Wood said. "I want to acknowledge those members of the public who got involved. They were significantly brave people."

Video showed people pinned the man to the pavement on his back with a plastic milk crate over his head and two chairs over his body.

Wood said it appeared the attack was unprovoked. The man "attempted to stab multiple people. Those attempts, thankfully, were unsuccessful," Wood said.

Police have shut down Sydney's central business district as they investigate the stabbing that left one woman dead and another wounded. (Matt King/Getty Images)

Uber driver Leon Baghani said the man, clutching a knife, jumped on the hood and then the roof of his Mercedes as he was driving an elderly couple on the street where the violence occurred.

"For a second, I thought maybe he's wearing a vest of some sort and he's going to detonate himself," Baghani told Ten Network television. "So I quickly accelerated and made a left turn and made sure that he came off the roof of the car."

A witness told reporters that the man was screaming comments about religion, before yelling to police that he wanted to be shot. Police said he used the Arabic phrase "Allahu akbar."

'Didn't show any remorse at all'

A witness, Paul O'Shaughnessy, said he and his brother Luke were working in the office of their recruitment company when they heard shouting through an open window. They looked out and saw a Caucasian man screaming "extremist" words, O'Shaughnessy said.

The brothers, fearing the man was conducting a terrorist attack, ran down to the street and began chasing the man, who was covered in blood.

Luke O'Shaughnessy and another man caught up with the offender and tackled him to the ground, Paul O'Shaughnessy said. Along with other passers-by, they used a milk crate and a chair to keep him pinned to the ground, he said.

Paul O'Shaughnessy told The Associated Press the man "didn't show any remorse at all."

Fuller said the assailant had a "history of mental health problems" and he would be charged.

Prime Minister Scott Morrison said on Twitter the violence was "deeply concerning" and praised the people who restrained the assailant.