At midday on Monday, the benchmark S&P/ASX200 index was up 14.9 points to 8,780.3, a gain of 0.18 per cent, while the broader All Ordinaries had gained 21 points, or 0.24 per cent, to 8,985.4.
The US bombed Iran twice over the weekend in what officials said was a response to an Iranian drone strike on a cargo ship in the Strait of Hormuz, testing the 11-day ceasefire, but Reuters reported that both sides had agreed to halt their attacks on each other for now.
"Back and forth, back and forth, the war in the Middle East is like a tennis match that just won't end (a hybrid cricket/tennis match?)," Kiwibank economists Jarrod Kerr, Alexandra Turcu and Elliott Lowe wrote in a note.
But despite the fresh hostilities, markets are pricing in a peace deal as highly likely, and quite a few oil tankers managed to get out of the strait during the small window of peace, the trio added.
At midday, six of the ASX's 11 sectors were higher and five were lower.
The technology sector was the biggest gainer, climbing 3.5 per cent after sinking 5.2 per cent last week.
Wisetech Global had climbed 4.2 per cent, Xero had added 5.1 per cent and Life360 had climbed 11.1 per cent.
The utilities sector was down 2.6 per cent as pipeline operator APA Group fell 4.6 per cent and Origin Energy lost 2.0 per cent.
In health care, Neuren had surged 28.1 per cent to a five-month high of $15.63 after the European Union recommended approval of its DAYBU treatment for patients with the rare neurodevelopmental disorder Rett Syndrome.
In the mining sector, Ramelius Resources had gained 2.2 per cent to $3.065 after the gold miner agreed to sell its shuttered Edna May gold mine in Westonia, WA, to Forrestania Resources for $300 million in cash and shares.
Forrestania shares were in a trading halt as the company prepared for a capital raising to fund the acquisition.
Other goldminers were mixed, with Northern Star down 1.9 per cent and Evolution up 0.6 per cent as the precious metal changed hands at $US4,080 an ounce.
As for the iron ore giants, BHP was down 0.1 per cent, Rio Tinto had dropped 1.3 per cent and Fortescue had added 0.4 per cent.
Energy Transition Minerals had dropped 23.1 per cent to a year-and-a-half low of four cents after the Greenlandic government refused its request to extend an exploration license that covers its proposed rare earths project in the Danish territory.
In the financial sector, Westpac and CBA were basically flat, while ANZ had dropped 0.4 per cent and NAB had added 0.5 per cent.
In the consumer discretionary sector, Accent Group had dropped 0.7 per cent to 70.5 cents after the shoe retailer urged shareholders to reject a 65-cent-per-share, zero-premium takeover offer from UK-based Frasers Group.
The Australian dollar was trading for 68.90 US cents, from 68.93 US cents at 5pm on Friday.