A spokeswoman for state-owned Kiwibank said it sent letters to 3000 customers at the end of May and gave customers 14 days to respond with their required information about their overseas tax status.
It began freezing accounts from last Tuesday has put 180 on ice already.
"This is an ongoing process and over the next two weeks we expect to freeze a total of 1900 accounts impacting 1200 customers."
The spokeswoman said funds in a frozen account would stay in the account but would not be accessible to the customer.
"This means the customer will not be able to carry out transactions on the account until they provide the additional information requested."
ANZ, the country's largest bank, said it froze accounts for about 200 customers last week and would continue to freeze accounts weekly as required by the IRD rules.
"We expect customer numbers for freezing to increase initially, but then reduce after a couple of months.
"We've been attempting to contact a number of our customers to resolve this position and many have recently been in contact with us."
ASB bank said as of the end of Friday it had put about 40 accounts on hold.
"We haven't closed any accounts, but by the end of [Friday June 29] we will have put approximately 40 accounts on hold.
"Nothing happens to the money in the accounts, it stays there until the customer contacts us and we can verify their tax details."
But two other major banks would not give details on how many accounts they had frozen.
A Westpac spokeswoman said it had not closed any accounts but had put some on hold.
"We cannot comment on numbers."
The spokeswoman said it had tried several times to contact customers to have them supply the required information.
"To comply with the legislation, Westpac NZ is required to place a hold on these accounts until the necessary documents are provided. Once this is completed, the hold will be lifted."
A BNZ spokesman said it had sent affected customers two letters, emails where it had email addresses, posted alerts on their internet banking login page and, in many cases, phoned customers.
"While we've heard back from almost all our customers, some haven't yet responded.
"In these circumstances, we are required by law to deactivate these accounts."
The bank did not respond to a request for the number of frozen accounts but said any customer who found their account deactivated should get in touch.
"We'll work with them to reactivate their accounts as soon as possible.
"If an account is deactivated, funds remain in the account. Once the customer has provided their tax residency information and it is validated by BNZ, the account is reactivated."
An NZBA spokesman urged people to respond to any request for information even if they weren't foreign taxpayers.
"A non-response isn't enough."
ON ICE: The number of frozen accounts
Kiwibank: 180 (1900 provisionally expected over next two weeks)
ANZ: 200
ASB: 40
Westpac: unknown
BNZ: unknown