A majority of economists believe quarterly inflation will rise 0.5% in June to take the annual rate to 1.1%, a figure last seen in June 1999.
BNZ markets economist Stephen Toplis said that if forecasts were correct, the Reserve Bank would be testing both edges of its 1% to 3% inflation band over the next 24 months.
"For the immediate term, it's a question of whether annual headline CPI (consumers price index) inflation can avoid dipping below the bottom of the band.
"We now believe it will probably sidestep this fate - but only on the technicalities of the recent move back up in fuel prices, along with the greater-than-expected jump in June's food prices."
The BNZ had forecast inflation would rise 0.6% in June, taking annual inflation to 1.2% from 1.6% in March. Mr Toplis said that would make inflation appear benign but he noted it would owe a lot to the high New Zealand dollar suppressing the price of imports, free-falling prices of electronic and telecommunications equipment and correcting commodity prices through the quarter.
"Underneath it all, we believe inflation is firming up.
"As a guide to this, we'll be taking greatest interest in the core components - the bits that aren't greatly influenced by the exchange rate and world prices."