The other banks have not yet said who they would put at the top of the queue.
Bruce Thompson, spokesman for Kiwibank, said hundreds of people had called to see what their options were since the limits were revealed.
Mr Thompson said the bank was looking to grow its share of the market so it could accommodate more lending to New Zealanders wanting to buy their first home.
A spokeswoman for ASB said customers had been in touch seeking clarification on how the new regulations would work. Late last week, the bank announced a special six-month fixed rate of 4.75 per cent per annum, its lowest ever home loan fixed rate.
However, that rate was subject to customers having at least a 20 per cent deposit, among other conditions.
BNZ and ANZ said they have had some inquiries from customers on how the new limits might affect them. Westpac did not answer the Herald's question on whether they'd had an increase in inquiries.
Jay Suchak, a Barfoot & Thompson real estate agent in Te Atatu, said a number of people had been through the firm's doors in a rush to buy.
Te Atatu is a popular area for first-home buyers in Auckland, but Mr Suchak said some customers were already finding it difficult to get approval for loans with less than a 20 per cent deposit, even though the new restrictions don't formally come into effect for more than a month.
New Zealand Bankers' Association chief executive Kirk Hope said people should be aware they may be declined loans because of the new restrictions and advised people to talk to their bank about individual needs and circumstances.
As well as first-home buyers and home-owners seeking a top-up loan for renovations, the restrictions would also affect businesses and householders seeking low-equity loans.
Banks would not risk their registration by breaking their obligations and would comply with the new lending requirements, Mr Kirk said.
New loan limits
*Banks will have to restrict the amount of loans they give to people with less than a 20 per cent deposit to 10 per cent of their total new lending each year.
*Some will choose first-home buyers over other borrowers but others say they will prioritise their existing customers first. Commentators say banks will pick people with lots of equity, high incomes and secure jobs.
*Changes come into effect on October 1.