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The 26-year-old was in a stable condition in Dunedin Hospital last night after undergoing surgery for stab wounds to her neck and face.
A scene examination of the cordoned-off Duncan St, City Rise, flat was carried out last night by forensics and CIB staff and was expected to resume this morning, Detective Inspector Kevin Hooper said.
The woman answered her front door about 8.30am and had a brief chat with a male stranger, who then stabbed her after getting inside the flat she shares with her 3-year-old daughter.
She managed to fend off her assailant and left the flat with her daughter, who was unhurt.
Det Insp Hooper said a passing motorist saw the woman "in a distressed state" and took the victim and her daughter to hospital.
Police had spoken briefly to the woman before her surgery and, despite her injuries, she was able to provide information about the attack.
"She is extremely lucky ...
"this is extremely serious and it is fortunate the stab wounds didn't go a bit deeper."
Det Insp Hooper said early indications were the man had chosen the house at random.
He declined to name the weapon used in the attack, or whether it belonged to the man or was sourced from his victim's home.
"What we know is she suffered stab wounds. I have an idea of what may have caused those stab wounds, but we don't want to go into it."
He declined to say if the attack was sexually motivated.
The man was described as light-skinned and about 184cm tall, with short hair and facial stubble. He was wearing jeans and a black hoodie.
Twenty police staff were investigating the attack. They were not looking at a particular suspect and were keeping an "open mind", Det Insp Hooper said.
Police had increased patrols around City Rise and would be canvassing the area again today.
"I would be asking people to use their common sense and be mindful of their personal safety. If anyone saw anything suspicious, not only between 7am and 9am [yesterday] but any time over the last few weeks, we would be interested in hearing about it."
Residents were asked to check their properties for "anything that shouldn't be there", as the offender had left the scene in an unknown direction.
Duncan St residents, including those who flat in the same building where the attack took place, said they had heard nothing until the large police presence arrived.
One resident said the woman was believed to have recently relocated from the North Island, but police were not able to confirm that last night.
Anyone with information can contact Dunedin police on 471-4800 or ring the anonymous Crimestoppers line, 0800 555 111.