Special rates apply to those with a minimum 20% equity and are also available for first home loan customers.
Kiwibank is also cutting its standard one- and two-year fixed mortgage rates to 5.69% and 5.79% respectively.
Term deposit rates are being trimmed by between 10-15bps. Its new two-year rate dropped to 3.80%.
Kiwibank said there was no change to its six-month term deposit, which has a limited-time interest rate offer of 4.10%.
The Reserve Bank makes its next OCR decision on August 20.
Market expectations are for a 25bps cut from 3.25% to 3%.
Since August last year, the OCR has fallen 225bps.
The Kiwibank economics team said this week the OCR will need to go to 2.5%, eventually.
Yesterday, the Bank of New Zealand announced it was cutting most of its home lending rates.
Its one-year and 18-month fixed home loan rates were cut by 10bps to 4.79%, while its two-year fixed rate decreased 6bps to 4.89%.
BNZ chopped 20bps off its six-month fixed lending rate, taking it to 5.09%.
Its three-year fixed home loan rate moved from 5.09% to 4.99%.
On Monday, the country’s largest bank, ANZ, cut its six-month special to 5.14% and its two-year rate to 4.89%.