BNZ says it may close the accounts of customers who are using payments to send abusive messages.
The bank said an internal review has found around 2000 monthly transactions that contain problematic use of payment reference fields, mostly containing swear words or other abuse. In some cases, people were using child support payments to facilitate harmful messages.
"It's actually really tough because what we don't want to do is block payments," said BNZ general manager for customer assist Martin King.
He said that instead, the bank would reach out to affected customers to offer support, and encourage people sending abusive payments to stop. If they refused, the bank would explore shutting their accounts down.
"Banks across the world are waking up to what their technology unfortunately can be used for," he added.
King said abusive payments are sometimes used to circumvent blocked communications on social media or SMS.
BNZ found around 20 transactions per month were of such low value that they were only being sent to send these messages.
The bank is also developing online filters for payments to try to reduce harmful messages.