The S&P/ASX200 rose 12.6 points, or 0.15 per cent, to 8,561, as the broader All Ordinaries gained 17 points, or 0.21 per cent, to 8,793.4.
While the Israel-Iran conflict continues, Reuters reports Iran is seeking a ceasefire and is open to making concessions to its nuclear program.
US President Donald Trump's sudden exit from G7 meetings in Canada has been linked both to a potential ceasefire and an escalation of conflict after he urged citizens of Iran's capital Tehran to evacuate immediately.
All three major Wall Street indexes pushed higher overnight as oil prices eased, but markets typically struggled to price geopolitical risk, Capital.com market analyst Kyle Rodda said on Tuesday.
"Based on Wall Street's overnight rebound, there are hopes any conflict will be contained, especially as Iran makes overtures about its willingness to negotiate a deal," he said.
Nine of 11 sectors, led by a 0.9 per cent push in IT stocks which followed a strong Nasdaq performance overnight.
Energy stocks eased 0.3 per cent after rocketing almost ten per cent higher in the previous two sessions, as investors tempered their worse-case scenarios for Iranian export infrastructure.
Oil prices briefly slipped below $US70 a barrel overnight but have since edged higher to $US72.88 a barrel, roughly on-par with early April, when US tariff announcements pummelled crude demand expectations.
Uranium plays have continued to soar following Sprott Physical Uranium Trust deal to acquire approximately 1.5 million pounds of uranium, sending Paladin (+5.0 per cent), Boss Energy (+6.7 per cent) and Deep Yellow (8.6 per cent) higher for a second day.
Boss and Paladin were the top-200's best performers.
The banking sector continued to take a breather after hitting a record peak last weak, with financials down almost 0.1 per cent and on track for a fifth straight session of gains.
Westpac was the big four's weakest performer, down 0.7 per cent to $32.96, while the Commonwealth Bank was slightly below flat at $179.38 a share.
Materials stocks gained 0.2 per cent, as large cap miners BHP (-0.4 per cent) and Rio Tinto (+0.1 per cent) struggled against continued weakness in iron ore prices.Â
Iron ore futures are trading at $US04.65 a tonne, their weakest price since September 2024.
Gold miners were back in the green after selling off on Monday, after investors repositioned from the safe haven following panic buying when Israel launched its first attacks on Iran on Friday.
The precious metal is trading at $US3,415 ($A5,235) an ounce, roughly 2.6 per cent short of its $US3,500 peak set in April.
Traditionally defensive consumer staples stocks gained 0.5 per cent, helped by a two per cent lift in Dan Murphy's owner Endeavour.
The Australian dollar is up against the greenback, buying 65.23 US cents, up from 65.06 US cents on Monday at 5pm.
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