The benchmark S&P/ASX200 index posted its best performance in nearly two weeks on Tuesday, climbing 99.4 points, or 1.17 per cent, to 8,604.7.
The broader All Ordinaries gained 94.1 points, or 1.08 per cent, to 8,829.5.
In Washington, Mr Trump said he had shelved plans for a "scheduled attack of Iran tomorrow" after appeals from the leaders of Qatar, Saudi Arabia and the United Arab Emirates.
"Serious negotiations are now taking place," Mr Trump wrote in a social media post, while adding the US was ready to go forward with another attack on Iran "on a moment's notice".Â
Domestically, two long-running surveys conducted by ANZ and Westpac revealed on Tuesday that consumer sentiment has ticked up recently as a spike in fuel prices eased.
Overall, however, consumers remained deeply pessimistic, said Westpac economist Matthew Hassan.
Minutes from the Reserve Bank released on Tuesday suggested the central bank would be inclined to leave interest rates on hold in June after hiking rates at its past three meetings.
Nine of the ASX's 11 sectors finished higher, with consumer staples the biggest gainer, climbing three per cent after a US broker put a bullish target on Woolworths.
The supermarket giant climbed 3.7 per cent to $34.21 after JPMorgan put a $37 price target on WOW shares, while rival Coles grew 2.7 per cent to $21.41 and alcohol retailer Endeavour added 2.3 per cent to $3.09.
In the financial sector, all of the big retail banks finished in the green.
Westpac added 1.9 per cent to $36.39, NAB grew 2.0 per cent to $37.04 and both ANZ and CBA advanced 1.3 per cent, to $35.52 and $162.88, respectively.
Insurance companies performed even better, with QBE advancing 2.9 per cent, IAG gaining 2.3 per cent and Suncorp rising 2.1 per cent.
In the heavyweight mining sector, Lynas Rare Earths declined 4.3 per cent and lithium miner PLS Group lost 1.3 per cent, while the iron ore giants managed to claw back most of their morning losses in afternoon trading.
BHP finished down 0.1 per cent to $58.70, Fortescue dipped 0.3 per cent to $21.88 and Rio Tinto dropped 0.2 per cent to $178.66.
In the communications sector, Singaporean mobile phone operator Tuas rose 17.6 per cent, clawing back some of Monday's massive 62.8 per cent plunge that followed word its Simba subsidiary may have been using unauthorised radio frequency bands.
In tech, Technology One dropped 2.9 per cent to $27.80 after the software company delivered a half-year profit after tax of $66.8 million, up six per cent from a year ago.
The Australian dollar was trading for 71.34 US cents, from 71.48 US cents at 5pm on Monday.
ON THE ASX:
* The S&P/ASX200 climbed 99.4 points, or 1.17 per cent, to 8,604.7
* The broader All Ordinaries gained 94.1 points, or 1.08 per cent, to 8,829.5
One Australian dollar trades for:
* 71.34 US cents, from 71.48 US cents at 5pm AEST on Monday
* 113.47 Japanese yen, from 113.58 Japanese yen
* 61.30 euro cents, from 61.43 euro cents
* 53.24 British pence, from 53.52 British pence
* 121.80 NZ cents, from 122.23 NZ cents
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