Reserve Bank board members said a lift in the unemployment rate and stagnant inflation could warrant a cash rate cut, but conditions did not justify reducing it from a record low 1.5 per cent this month.
The minutes of the RBA's April 2 meeting showed board members noted the labour market had strengthened in early 2019, though GDP growth had slowed beyond expectations.
"Members also discussed the scenario where inflation did not move any higher and unemployment trended up, noting that a decrease in the cash rate would likely be appropriate in these circumstances," the minutes released on Tuesday said.
"(Members) recognised that the effect on the economy of lower interest rates could be expected to be smaller than in the past, given the high level of household debt and the adjustment that was occurring in housing markets."
The board's minutes said on Tuesday the likelihood of a higher cash rate in the near-term was low, marking a dovish turn in policy compared to last month when it saw the risks for rates to move in either direction as more evenly balanced.
ANZ Head of Australia Economics David Plank said despite a subtle tilt, the RBA did not appear in any hurry to make a decision, and looked as though it needed a convincing case to ease.
CommSec's Craig James said it seemed the Reserve Bank expects further progress in reducing unemployment, lifting wage and prices, and therefore lifting consumer spending.
JP Morgan rate strategy analyst Sally M Auld said the RBA may even be a little more pre-emptive this cycle, given the proximity of the lower bound and the reduced potency of rate cuts.
The Aussie dollar dropped on the release of the minutes at 1130 AEST, falling from from 71.70 to 71.41 in the space of 45 minutes.
In Tuesday's minutes the board said a lower interest rate could support the economy through a depreciation of the exchange rate and by reducing required interest payments on borrowing, freeing up cash for other expenditure.
The cash rate, which reflects what the central bank charges commercial banks on overnight loans and influences all other interest rates, was last cut in August 2016 and hasn't been hiked since November 2010.
Fresh jobs data is expected on Thursday, while first quarter inflation data will arrive later in April.