Manukura has recovered from treatment for swallowing stones earlier this year.
A small number of North Island brown kiwi carry a recessive gene which both male and female birds must have to produce a white chick.
Department of Conservation captive breeding ranger Darren Page said it was remarkable that two birds with the rare white gene had paired up in 940ha Pukaha Forest to produce two white chicks in consecutive seasons.
There is only a one-in-four chance of a pair with the rare gene producing a white chick.
Mr Page said the probability the pair would breed again was quite high.
"But we have no influence over the pairing and no way of knowing if they produce more chicks - unless they are white."
The parents of the white chicks were both among 30 transferred from Little Barrier Island last year to boost the adult population at Mt Bruce.
The white gene is thought to have found its way into the kiwi population on Little Barrier after a white kiwi was put on the island early last century.
Jason Kerehi, a Mt Bruce board member and chief executive of Rangitane o Wairarapa, the iwi that named Mauriora, said the name was a powerful one, used as an exclamation or definition of something important.
"This new kiwi is seen as an assurance that we are blessed with more than one special creature and there is potential for more."
Eleven kiwi have hatched at Mt Bruce this season, and more are expected.
Of two kiwi eggs now incubating in the nursery, one is from the same nest as Mauriora.
- APN