Reserve Bank of Australia deputy governor Andrew Hauser said the consumer price data released by the Australian Bureau of Statistics on Tuesday was "very welcome".
The central bank's preferred measure of inflation, the trimmed mean, fell from 2.9 per cent to 2.7 per cent in the June quarter.
Mr Hauser said the RBA had been looking for more evidence that inflation was moving sustainably back to the midpoint of its two to three per cent target band.
"And we've had another piece of that jigsaw yesterday," he said in a fireside chat with Barrenjoey chief economist Jo Masters on Thursday.
The RBA wanted to make sure it brought down inflation to its 2.5 per cent target in a way that was "gradual, considered, measured ... predictable," Mr Hauser said.
His comments echoed minutes from its board's July meeting, in which most members declared back-to-back rate cuts would not be consistent with a "cautious and gradual" monetary policy strategy.
The RBA's decision to hold the cash rate at 3.85 per cent did not prove particularly predictable, blindsiding markets and the analyst consensus.
But money markets and economists widely expect the central bank board to lower the cash rate to 3.6 per cent at its meeting in August.
Another interest rate cut would be "welcome relief" for mortgage holders, Treasurer Jim Chalmers said.
"But it's never mission accomplished because the global environment is uncertain - we've got some persistent structural issues in our economy, growth in our economy is soft, and people are under pressure," Dr Chalmers told ABC TV.
Despite rising real incomes, falling interest rates and tax cuts, consumer spending had persistently undershot the RBA's forecasts since the start of the year, Mr Hauser said.
The clue might lie in weak consumer confidence.
The amount of momentum in the economy was an area of debate among the RBA board, Mr Hauser added. Some who believed interest rates should be lower worried that consumer confidence could continue to lag, he said.
Retail data released shortly after Mr Hauser's remarks suggest consumer spending may have turned a corner, with turnover jumping 1.2 per cent in June, tripling consensus estimates and solidly beating May's upwardly revised 0.5 per cent rise.
"The strong June month rise in retail turnover was driven by discounts linked to sales and new product releases," said ABS head of business statistics Robert Ewing.
"Turnover for electrical and gaming retailers was lifted further by the much-anticipated launch of the Nintendo Switch 2, which delivered record sales."
While consumer confidence had been rattled by global trade tensions, Mr Hauser suggested three reasons why the impact of US President Donald Trump's tariff threats had not been as bad as feared.
Firstly, the worst of the threatened tariff outcomes had not eventuated, especially retaliatory measures by other countries. Second was the Australian and global economies being more resilient than expected.
More worryingly, a third reason could be that the worst impacts are yet to come.
"You may remember when Brexit occurred, everyone rushed to the exit gate and nothing happened," Mr Hauser said.
"But my goodness me, 10 years on, I think it's fair to say things are happening.
"If those tariffs stick, there's a real tax increase, and someone has to pay it."
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