First Union said the move puts up to 100 jobs at risk, although there could be some redeployments.
A decision would be made once feedback on the proposal from staff had been evaluated, the bank's statement said.
"Staff and customers will be the first to know that decision and there will be no further public comment until then," the statement said.
First Union said the branches included in the proposal to close were mostly rural and in small communities.
According to First Union the branches that could be closed were: Kamo, Whangarei; Broadway Avenue, Palmerston North; Bishopdale, Christchurch; Gardens, Dunedin; Waikanae; Carterton; Raglan; Ranfurly; Te Aroha; Fendalton Mall, Christchurch; Putaruru; Whangamata; Takaka; Stoke; Wainuiomata; Te Anau; Fairlie; Otorohanga; Cherrywood, Tauranga.