ANZ, the country's largest bank, said it would cut 10 basis points of its floating and flexible home loan rates and between six and 14 basis points off its fixed term rates.
Antonia Watson, ANZ managing director of retail and business banking, said fixed home loan rates had fallen steadily since the last OCR cut in 2016.
In March 2017 the bank's one year fixed special rate was 4.39 per cent and now it would be 3.89 per cent.
Watson said the low interest rate environment presented opportunities for borrowers.
"The current extreme low interest rate environment not only represents an opportunity for new home buyers to enter the market, but for existing home loan customers to pay off as much of their debt as possible."
But it will also cut its term deposit rates shaving 15 basis points off its 90 day term rate and 25 basis points of its 60 and 120 day term deposit rates.
"It's important that people maintain healthy savings, but a lower cash rate will impact on deposit interest rates."
Watson said it was concerned people might seek higher interest rates through riskier investments and savings options.
"Lower deposit interest rates will also be a concern for the elderly who rely on interest income in retirement."
Kiwibank also cut both mortgage and deposit rates.
It will cut its floating home loan rates by 15 basis points to 5.65 per cent for those on a variable rate and offset rate and 5.7 per cent for those on a revolving retail rate.
But will also slice 15 basis points off many of its term deposit rates. Its 90 day rate will fall to 3.1 per cent and its 32 day saver rate will fall to 2.1 per cent.
Online call and business online call account rates will also fall 15 basis points.
Mark Wilkshire, Kiwibank chief marketing officer said it was good news for customers with variable home loan products.
"We are making these changes so that our home loan customers get the benefit of market changes."
The changes come into force for new customers of the banks from May 13 and existing customers on May 27.
