The police have a huge list of people of interest as they continue to hunt who killed a 69-year-old woman in her own home, they say.
The investigation into who attacked Cun Xiu Tian in Te Atatu in Auckland is now in its fifth day.
Family members found the grandmother dead when they got home from work on Friday.
The police have called it a despicable crime in which Ms Tian suffered a horrific death, and said a great force was used to strike her about the head and face many times.
In his latest update to the media, Detective Senior Sergeant Roger Small said it was still not known if there was more than one attacker.
"We're doing everything we can to bring those responsible accountable.
"I would like to reassure the community that we're doing everything to bring those people to justice," he said.
Mr Small said names of people of interest have been put forward from across the country.
"We're keeping a very open mind in regards to where the offender might be.
"I can tell you that I've had nominations from all over the country in regards to persons of interest.
"So it's happened in Te Atatu Peninsula - that was always going to be the point where we start.
"But we keep a very open mind, in regards to it's so easy for people to be so mobile today and travel the length of the country and overseas," Mr Small said.
A candlelight vigil will be held at Te Atatu Baptist Church at 7pm near Ms Tian's home.
Residents urged to look for discarded clothing and suspicious behaviour
The police said the examination of Ms Tian's home and the post mortem on her body suggested it was highly likely her attackers left with blood on them, their shoes or their clothing.
Mr Small said her attacker or attackers may have tried to wash themselves, or get rid of or burn their clothing.
"We ask that people be particularly vigilant around friends, family members, associates and flatmates that may have come home after 9am on Friday last week.
"We also ask that people walking through parks and past public rubbish bins be vigilant.
"If they see any discarded clothing or shoes (with) blood on them, in particular around the West Auckland area, we want to hear from you," he said.
Police have spoken to more than 300 residents in more than 125 homes in and around the Te Atatu area.
They said they were collating hundreds of hours of CCTV footage, and officers would remain at Ms Tian's home for another week or more.