Speaking after the bank delivered its half-year net profit of $416 million, an 8 per cent drop on the same prior period, Healy said it was starting to see a softening in the property market.
But demand for loans remained higher than deposit growth which meant banks were having to pay more for deposits resulting in those costs being passed through to borrowers.
"I think there will continue to be pressure on mortgage rates. Banks have seen a compression of margins and that is going to continue," he said.
BNZ's net interest margin dropped 12 basis points to 2.15 per cent during the half year to March 31.
So far this year banks have increased their mortgage rates incrementally with some moving them up at 5 or 10 basis points every few weeks.
Healy said that was likely to continue.
Healy said a softening in the property market was good thing but he said it would be a worry if construction growth were to slow further.
While housing affordability continued to be an issue, he said the biggest risks to the bank were unknown factors such as the volatility in global markets, the twists and turns in US politics and what was happening in North Korea.
Healy also pointed to growing global regulation of banks which could increase how much capital they have to hold.
"Banks are waiting to see if new benchmarks will be higher."
If they are increased, that could result in banks having to raise more capital. If it all comes at the same time, that could mean more competition for funding which could push up costs.
New capital regulations were expected to be announced in the next 12 months, he said
While the bank's net profit fell, its cash earnings rose $40 million to $484m.
Deposits at the bank increased by $4.2 billion or 8.6 per cent to $53b over the half while loans and acceptances increased $5.1b or 7.2 per cent to $76.2b driven by housing and business lending.
Healy said it had focused on sustainable growth in the mortgage market by growing its business via brokers which had seen a boost of $900m in broker home loans this year.
The bank's net interest income increased by $25m or 3.1 per cent in the half, driven by growth in lending an deposit volumes partly offset by lower margins.
BNZ's operating expenses increased $3m or 0.7 per cent while its charges for bad and doubtful debts fell by $44m as a result of improved economic conditions including the outlook for dairy.
Healy said the BNZ maintained a robust capital structure, with a strong balance sheet that is well funded through diversified and stable funding sources.
BNZ's Core Funding Ratio of 85.59 per cent exceeded the Reserve Bank of New Zealand minimum requirement of 75 per cent as at March 31.