It is understood James has close family who live in Te Puke, including a half-brother and three half-sisters. Other relatives live in the wider Tauranga area.
James' uncle said his nephew would be sadly missed.
The 5-year-old's mother, Mui May, said she was struggling to believe her son was dead.
She broke down in tears as she told Samoan television: "I was shocked when my older sister rang me and told me James was gone."
Police said yesterday the 8-year-old cousin would not be charged.
An uncle who was hunting with the children had been taken into custody. He is likely to face charges of possession of an unregistered firearm.
James' funeral is set for some time this week.
It is understood James was not a Kiwi citizen and neither is his mother, Mui May. However, the New Zealand High Commission in Apia is assisting the family as Mr May is a Kiwi.
Police said the 8-year-old boy was no longer in police custody, but had not been sent back to his parents and was instead with members of his extended family.
Mr Pula said the incident had once again highlighted the issue of unlicensed guns in the island nation.