Father Thomas Phillips and his three children Jayda, Maverick, and Ember, have been missing since December last year from the Waitomo area.
A warrant was issued for Phillip's arrest after he failed to appear in court in January for a charge of wasting police time and resources.
The children's family members raised more than $4500 through Givealittle for a reward and have supplied the rest of the money themselves.
In a social media post last month, the children's family celebrated Maverick's 8th birthday.
"We hope that wherever you are, you have had an exciting, fun-filled day," the post said.
"We hope you are happy and healthy. We hope you had a yummy strawberry cake with candles to blow out. We hope that Jayda and Ember gave you lots of hugs and kisses from us. We hope to see you all soon. We love you."
The post said: "It would be a Christmas blessing to have these children back, safe and sound."
Phillips and his three children went missing in 2021 for three weeks, and after a land, sea and air search had failed to find them, the family walked out safe and well having been been living in a tent in dense bush.
Anyone with information can contact police quoting case number 211218/5611 or anonymously via Crime Stoppers on 0800 555 111.
Mayor in no doubt someone aiding Tom Phillips
Ōtorohanga mayor Max Baxter urged Tom Phillips to come back with the children in time for Christmas so they could celebrate it with their relatives and friends.
"Wouldn't that be great - if all the family was together for Christmas," he told Checkpoint.
The impact of their disappearance on the family must be immense, he said.
"For the family absolutely devastating at this point... Somebody knows their whereabouts I have no doubt... I can't imagine you could be missing for a year without some assistance from somewhere."
At some stage the person or people helping Tom Phillips needed to be sensible and consider the interests of the extended family, Baxter said - and added that a year was a long time in the children's development.
"Just say we've had enough now and it's now time to return the children back to where they should be."
While the police believed the family could be living in some kind of structure or camp, Baxter said it had been a very wet winter and spring and it would be "incredibly challenging" to survive in some kind of makeshift shelter.
He was amazed that the children had been able to survive away from civilisation the first time they went missing.
"It's a huge expectation to ask for anybody let alone children who haven't even reached the age of 10 years."
He hoped the sum being offered for information might be enough to help lead to a resolution.