Aisling Symes, two, has not been seen since she was walking near her home in Longburn Rd, Henderson about 5.30pm on Monday.
Police say there is no evidence she has been abducted but they are treating it as more and more likely after searches for her have turned up nothing.
Aisling's aunt Aithne Potts today described the girl as bubbly and social and a girl who loved to dance and to dress up dolls.
She said she loved her food and had a large extended family and church community, so she might well take help from anyone who offered it.
Ms Potts was holding back tears as she called for Aisling to be returned if she was being held.
"If you are the person who has my niece, we don't understand why you wouldn't have told us," she said.
"We don't understand why it is so long and we know nothing.
"So please, tell us where she is. We just want her home."
Waitakere police area commander Inspector Gary Davey said police now believed she was not within a 3km radius of where she disappeared.
"The search is not over and it's not complete, but having said that we are confident she is not within those boundaries," he said.
Mr Davey said he would now like anyone who was within 5km of where she disappeared to thoroughly search their properties in the chance that Aisling was there.
Mr Davey earlier today said police were still treating Aisling's disappearance as a missing person inquiry.
"There is still no evidence that anything untoward has happened to Aisling," he said.
"But given the extensive nature of the search and the fact that there has been no further sightings or no discovery of her items, the investigation side of the inquiry is increasing."
Mr Davey said police still wished to speak to an Asian woman in her mid 30s who was seen touching Aisling on the back while walking her dog when Aisling was last seen.
Anyone with information about Aisling's disappearance or the Asian woman is asked to call police.
