The police probe continues and is focussing on establishing the movements of the alleged offender in the hours and days leading up to last Thursday's incident.
Mr Williams, who is leading the inquiry, says investigators have been speaking to witnesses, as well as family and contacts of the alleged offender.
"We've had a tremendous response from the public, and a large number of people have come forward with information about Thursday's events.
"We are now working through those interviews,'' he said.
The Christchurch City Council employee who suffered multiple stab wounds to the upper body in the incident is reported to be in a stable but improving condition today.
Police will interview him when he is sufficiently recovered, said Mr Williams.
Investigations into the actions of the three police officers involved in the shooting at Hoon Hay Road are continuing. All three officers have been interviewed by investigators, including the Independent Police Conduct Authority.
The shooting drama started around 7am last Thursday when a man was disturbed in the grounds of Redwood School by the caretaker.
After allegedly threatening the caretaker and a teacher, the man ran off and came across 36-year-old Marteine Robin who was doing a routine early morning delivery of pies to the school.
The knife-wielding man opened the passenger door of her truck and got inside.
He allegedly forced Ms Robin to drive at knifepoint, and stabbed her in the shoulder.
"I feared the worst, I thought I was going to die,'' Ms Robin said.
Ms Robin eventually managed to escape when the man was momentarily distracted at a traffic jam almost one hour, and 50km later.
But the drama only escalated. Police say the man left the truck near the busy intersection of Hoon Hay and Halswell roads and then almost fatally stabbed the council worker who intervened.
Construction worker Jade Lynn, 22, was hailed a hero by keeping the knifeman at bay with a crowbar until police arrived.
The armed man was stopped only when pepper sprayed, tasered and then shot twice by a policewoman.
Armed with a Glock pistol, she fired two shots, one hitting the man's shoulder and the other his wrist.
Victim Support were called in to speak to the victims, and provide support for Mr Lynn.
Police have refused to confirm whether the shot man was known to police.
His family are said to be "absolutely devastated'' at the incident.
