The injured woman, 41, remains in a stable condition in hospital.
"We will allege the offender has attempted to stab multiple people, luckily unsuccessfully".
Police say they are investigating reports the man was heard yelling "allahu akbar" during the rampage. Police say the threat in Sydney's CBD is now over after a man was taken into custody. They approached a person with... clear evidence of a stabbing previously. A 21-year-old woman, now unidentified, was later found dead in a unit block nearby.
"I followed him up York St trying to get him to focus on me rather than anyone else", he told the Nine Network.
While the motive of the attack is not yet known, the man has been taken into custody, police said.
Australian Prime Minister Scott Morrison tweeted that the "violent attack" was "deeply concerning" but praised the "brave actions" of those who restrained the suspect.
Our counter-terrorist command immediately stood up and the joint CT team which includes police and state and fed agencies, have assessed all available info in relation to his crime and it is not now classed as a terrorism based incident.
According to the BBC, Lee Cuthbert, Paul O'Shaughnessy and Luke O'Shaughnessy ran out from their office when they heard the commotion and ran out to catch the man; and Luke O'Shaughnessy said he forced a "chair over the man's legs, a chair over his torso and then a milk crate on his face" to hold him down.
(Dean Lewis/AAP/via Reuters) An aerial view shows security officers standing around a barricaded area, following reports of a stabbing incident in the central business district of Sydney, Australia on August 13, 2019, in this still image from video obtained via social media.
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'The cops are here and they blocked the road right now, so we can't go outside.
He said while police weren't looking for any other offenders they couldn't discount coming across other crime scenes as the investigation continues.
Police have linked the murder of a woman to a stabbing rampage in central Sydney which left another woman in hospital.
"A short time later, members of the public detained the man before police attended and arrested him".
Superintendent Gavin Wood described them as "significantly brave".
A witness named David told ABC News about five or six people chased the man down.
"They were fearless and I can only use that word seriously - they were significantly courageous people", he said.
The attacks are not being treated as a terrorist attack, the New South Wales police commissioner, Mick Fuller, said on Tuesday night.
One witness, Marcon, told the Daily Mail Australia: "He was trying to smash a driver side window of a random auto with the knife".