The Reserve Bank of Australia said it would cut interest rates "if needed" at its July policy meeting, where it slashed the cash rate by a quarter point - the second cut in as many months - taking them to a record low of 1%.
The move highlighted the RBA's urgency to get the country's economy on its feet and reduce unemployment, and markets had already begun pricing in another 25 basis-point cut before the end of the year.
The S&P/ASX 200 index ended 0.2% lower at 6,641 points. The benchmark ended down 0.7% on Monday.
The RBA's dovish tone pushed down the yield on Australian debt, which gave a lift to defensive stocks - often seen as bond proxies.
The local utilities and healthcare sub-indexes each added 0.6% and 0.4%, respectively.
The mining sector pared gains after Rio Tinto shares reversed course to give up earlier advances, which rode on strong iron ore prices.
Earlier on Tuesday, Rio Tinto reported a fall in quarterly shipments and flagged a cost blow-out of up to $1.9 billion and a delay of up to 30 months at its Oyu Tolgoi underground copper mine in Mongolia, a key growth project.
The miner's shares ended 0.6% lower after gaining as much as 1%. Rio's larger rival BHP Group advanced 0.4%.
On the other hand, the country's biggest banks shedding between 0.04%-0.7% bruised the main board, while weakness in oil prices for a second consecutive day strained energy shares.
Woodside Petroleum, the energy sector's biggest constituent by weighting, was off 2.2% on the day.
New Zealand's benchmark S&P/NZX 50 index ended 0.1% lower at 10,651.20.
Data showed inflation accelerated in the second quarter due to higher fuel and housing costs, but it did little to change expectations of an interest rate cut this year.
Shares of Auckland International Airport down 2.3% and Fisher & Paykel Healthcare off 1.8%, were the biggest decliners.