The S&P/ASX 200 index closed 0.5%, or 31.1 points higher at 6,471.2. It lost 1.3% in the previous session when new retaliatory tariffs from U.S. and China had battered market sentiment.

Trump later on Monday flagged the possibility of a trade deal with China and said he believed Beijing was sincere in its desire to reach an agreement.

Iron ore is Australia's biggest export and China its top trade partner, making miners of the steel-making material especially sensitive to developments in the trade war.

Australian iron ore miners BHP Group, Rio Tinto Ltd  and Fortescue Metals finished between 0.8% and 5.3% higher, after sharp losses on Monday.

The country's banking stocks, the weightiest on the benchmark, also rose 0.5%. This was despite news that Australia's big banks will face potential penalties within the next six months for breaching money laundering laws.

Among the "big four" banks, Westpac Banking Corp closed flat, while the others gained between 0.4% and 0.9%.

High-growth tech stocks also surged 3.2%, following overnight moves from tariff-sensitive Wall Street peers such as Apple Inc.

U.S.-focused buy-now-pay-later firm Afterpay Touch Group  was the second biggest gainer on the benchmark, up 7.8%.

Medical tech firm Nanosonics topped gains, soaring 32.7% to close at a record high after posting record full-year sales and stronger profit.

Meanwhile, gold stocks bucked the trend to shed 3.2%, as the recovery in risk appetite led to a retreat from safe-haven assets.

The country's biggest gold miner Newcrest Mining Ltd  lost 1.5% while Northern Star Resources lost most, droping 6.6%.

Across the Tasman Sea, New Zealand's benchmark added 29.7 points or 0.3% to end at 10,513.1600.

Dairy giant a2 Milk Company Ltd added 1.3% while transport provider Tourism Holdings rose 5.3% and was the top gainer on the index.