The children have been named as August, Hugo and Goldie, aged 7, 5 and 1.
The Givealittle page has since raised more than $136,000 for their mother as she dealt with the "unimaginable loss".
"They were the light and love of her life, and her entire world has been shattered," the Givealittle page said.
"In the midst of this unimaginable grief, she also lost her home and everything she owned. She is facing the hardest journey possible, stripped of her physical security, while navigating the deepest emotional pain."
The search for the body of one of the children was continuing today, police said.
The bodies of two children were recovered last night and blessed by the family with karakia.
The body of the adult was removed earlier. Manawatu Area Commander Inspector Ross Grantham confirmed to RNZ's Morning Report programme today it was the children's father, which RNZ understood was Dean Field.
Police said their focus now would be on finding the third child's body.
"It's unimaginable, the tragedy for the families going through this," Grantham told Morning Report. "We are working very carefully through the scene to establish how it started, and that's still going to take us some time."
It was too early to tell yet if the fire was deliberately started.
"It's pretty risky with the part of the structure still there and the the dust that's generated from the fire, so it will take us some time just to go through and establish what's happened."
Police were not seeking information from the public at this stage, but if anyone knew anything, they could "reach out".
He said it was "unusual" for a house fire to begin in the afternoon.
Police were not looking for anyone else in relation to the fire.
Neighbour describes seeing the fire as it happened
A neighbour told RNZ he was working at his home on Saturday when someone noticed smoke from a nearby property.
"We all came out to have a look and we saw a horrific amount of smoke coming from about 300 metres away, where the neighbour's house is - pretty thick black billowing smoke.
"It was a very, very windy day and we knew it wasn't any kind of controlled fire. We knew it was some sort of what we considered to be a house fire at that stage."
He said over an hour, many firefighters arrived and tried to put the blaze out.
An hour after it started, the blaze and billowing smoke was still visible. He believed it took two hours for firefighters to put the fire out.
"They were still dousing it down and there was just very slight wisps of smoke coming from the property two hours after it started."
He said State Highway 1 near the property did not open until 8pm on Saturday.
The neighbour said that, during the fire, he was "pretty shocked" at what was happening before his eyes.
"Nothing we could do about it and just a feeling of kind of despair, I guess just watching what was going on.
"Knowing that a young family was potentially losing everything they owned and knowing that is going to be a very, very hard place to come back from.
"Just the thought of not knowing whether everybody was alright or not, and subsequent to that we found out, that isn't the case, which has made things 10 times worse."
