The S&P/ASX200 closed 20.8 points, or 0.25 per cent, higher at 8,481.8, on Tuesday as the broader All Ordinaries gained 26.4 points, or 0.3 per cent, to 8,683.9.
The bourse pared back earlier losses following reports the Republican president had told aides he was open to ending the military campaign while the Strait of Hormuz remained mostly closed.
This followed reports Iran had struck a Kuwaiti oil tanker off Dubai.
The benchmark Brent crude oil price remains above $US100 a barrel but has tempered following the White House reports.
IG market analyst Tony Sycamore said the latest sign of de-escalation comes as US motorists face retail petrol prices above US$4 a gallon and the president's approval rating tanks.
"While Trump's desire to wind down the campaign quickly is understandable, the decision to defer the reopening of the Strait of Hormuz leaves a critical chokepoint firmly in Tehran's hands for the foreseeable future," he said.
"Unfortunately, this also pushes back any concrete resolution regarding the Strait's reopening, effectively extending the uncertainty weighing on markets and the broader global economy."
In Australia, investors learnt more about the split decision behind the central bank board's 0.25 percentage point interest rate hikes at the March meeting.
ANZ economist Adam Boyton said the lack of forward guidance suggests the board does not have a preconceived view on the next policy move, and weaker domestic data since supported the big four banks' prediction for a hold in May.
The Reserve Bank of Australia has also banned credit and debit card surcharges despite concerns voiced by banks and small firms.
In another regulatory development, the Fair Work Commission decided to scrap junior pay rates, adding to retail, pharmacy and fast-food operating costs.
Eight of the ASX-200's 11 sectors were higher, led by a rally in tech stocks as traders sought attractive deals.
Accounting tech firm Xero finished 6.5 per cent higher and logistics software company WiseTech global posted a 4.1 per cent gain.
Energy stocks closed lower after higher fuel prices helped them outperform other sectors in recent weeks, with Santos losing 1.1 per cent and Woodside down 0.5 per cent.
Miners broadly finished lower, with Fortescue down 1.2 per cent, to $20.31, and BHP falling 0.1 per cent, to $50.39.
Rio Tinto gained 0.4 per cent, to $161.43.
Banks were higher despite tighter surcharge regulation, with Westpac gaining one per cent, to $39.47, NAB picking up 0.5 per cent, to $41.44, and ANZ climbing 0.2 per cent to $35.97.
CBA stocks fell 0.6 per cent, to $167.70.
Mattress and sofa e-commerce retailer Koala made a successful debut on the ASX, with shares trading up 8.8 per cent from their $3.40 price during an initial public offering.
Shares in radio giant ARN dived 19 per cent as a second lawsuit was levelled at one of its subsidiary by morning radio heavy-weight Jackie "O" Henderson.
ON THE ASX:
* The S&P/ASX200 gained 20.8 points, or 0.25 per cent, to 8,481.8.
* The broader All Ordinaries lifted 26.4 points, or 0.3 per cent, to 8,683.9.
One Australian dollar trades for:
* 68.69 US cents, from 68.69 US cents at 5pm AEDT on Monday.
* 109.38 Japanese yen, from 109.67 Japanese yen.
* 59.77 euro cents, from 59.65 euro cents.
* 51.90 British pence, from 51.74 British pence.
* 119.92 NZ cents, from 119.65 NZ cents.
