Police said the mother-of-two had dropped her children off at Miramar Central School and was seen speaking with a teacher.
It was believed she took a short route from her Brussels St property to the school, along Park Rd, between 8.30 and 9am.
Police are appealing for anyone who saw Ms Fan or her red Honda hatchback, registration GSL128, after then.
She has been described as short with a slim build. Police said it is likely she was wearing a hooded crimson top with white stripes on the shoulders and plain black track pants.
Police would also like to hear from anyone who saw anything out of place or suspicious in the local area on that Friday morning.
"If you saw Mei at anytime on Friday we need to hear from you. Whoever has done this has taken away the mum of two little children which, anyway you look at it, is a heartless act,'' Mr van den Heuvel said.
"It could be the one small thing that you have noticed that could make all the difference to holding the person responsible for this to justice.
"We are continuing to speak to a number of people and are making great progress piecing together Mei's final movements.
"I can reassure the community that there is nothing to indicate that this is anything but a one-off attack resulting in the needless loss of a young mother's life.''
A 58-year-old Strathmore Park man, who knew Ms Fan, has been arrested for breaching a protection order against her.
He appeared in the Wellington District Court this week and was released on bail. The man was granted interim name suppression until his next court appearance next month.
A court charge sheet said the man had allegedly sent the woman correspondence sometime between Thursday and Sunday.
