"We were shocked and shaken to learn that far away in New Zealand one of our relatives, Mei, was killed in a violent attack. It is beyond belief and beyond comprehension," the family said.
"Mei was a beautiful, well-taught, helpful, respectful and caring daughter, and loving mother.
"The heartbroken news of her sudden death has brought us enormous grief, and will leave a permanent scar in her parents' and family's lives in China."
The family appealed for anyone with information to come forward to police "for the sake of her two lovely children".
"We hope the person or people responsible for Mei's death will one day be held accountable for what they have done, and her departed spirit can at last rest in peace."
The family said they were grateful for the compassion, help and care they had been given by the Chinese embassy and New Zealand police.
Mr van den Heuvel said the family was discussing the future of Ms Fan's two children. Police earlier said the family would make a decision on whether they would stay here or be taken back to China
Ms Fan's parents did not travel to New Zealand because of their age.
A team of 30 officers was working on the case and police were making good progress towards identifying Ms Fan's killer, Mr van den Heuvel said.
"We've told the family as much as we can. It's very important that they have a fuller picture of what happened.
"They understand Mei's death was tragic and violent and that we are doing everything we possibly can to bring her killer to justice, and that we have every confidence we will achieve that."
Mr van den Heuvel said police had spoken to Ms Fan's children as part of the inquiry.
"They have provided some information that has been useful to the inquiry and we continue to keep and eye on their wellbeing and their safety," he said.
"They are in the safe hands of family members and they have been reunited with their Chinese family when they arrived on Sunday."
Police had identified several people of interest to the investigation, but could not go into details.
"Obviously we look closely at the people that were close to Mei as part of our investigation."
Investigators were open-minded about how many people were involved in her death.
Police wanted to know more about the movements of Ms Fan's red 2005 Honda Fit hatchback car, registration GSL128, any time on November 8.
"We appeal to the public for sightings of this car please. We also continue to appeal for information from anyone who has seen anyone or anything suspicious in or around the Brussels St address on Friday the 8th of November or the days leading up to it," Mr van den Heuvel said.
Police divers last week found a number of objects of interest as the searched the coastline by the Miramar wharf and Shelly Bay Rd for items that may have been linked to the killing, such as clothing used as a disguise.
Police have also released an image of the 32cm knife with a wooden handle used to kill Ms Fan.
