The rates that act as an indicator for mortgage levels are continuing to fall, as demand for long-term fixed home loans eases.
The two-year swap rate has now fallen from a peak of 4.2% in late March to 3.8%, while five-year swap rates are under 5%.
Swap rates had been driven up by a surge in demand from households and firms to lock in low interest rates, prompting the Reserve Bank to reiterate earlier this month that interest rates would remain low for some.
A Reuters news agency poll found analysts expect the central bank to cut interest rate by at least a quarter of a percentage point at its next review, this month.