The S&P/ASX 200 fell 0.6% to 7,539.60 points by 1247 GMT to mark its worst day since July 28. The benchmark snapped a four-day winning streak to close 0.6% lower on Monday
Morning trading in Asia did not move majors much from those levels, with the euro last at $1.1902 and the yen at 110.58 per dollar. The Aussie bought $0.7517.
Kent reiterated that the bank did not expect domestic inflation to return to its 2-3% target band until 2024 at the earliest, so policy would need to stay very accommodative.
A sale would be tricky, though. The big four New Zealand banks - all Australian-owned - control almost 90% of the market, so are unlikely to be allowed to buy.
The kiwi dollar held firm at $0.7173, after finding support at $0.7150. It remains far from the January top of $0.7314 and has resistance at $0.7225 and $0.7246.
The S&P/ASX 200 index was up 1.1% at 6,725.70 by 2350 GMT, its best session since Jan. 19, after ending about 2% lower on Thursday. But it was on track to rise 1.7% in January, its fourth straight monthly gain.
The news took a toll on safe haven bonds with Australian 10-year futures falling 6 ticks to 98.9600, implying a yield of 1.04% and back toward a recent low at 98.9200.
The Brexit headlines overshadowed US President Donald Trump's demand for changes to a coronavirus aid bill, effectively threatening a government shutdown next week.
"A stronger than expected economy certainly goes in that direction, but this needs to be balanced against other developments such as the sharply higher New Zealand dollar."