The benchmark S&P/ASX200 index was up 2.7 points, or 0.03 per cent, at 8,582.8 about midday on Monday, having been down as many as 21.8 points in the first few minutes of trading.
The broader All Ordinaries was up 4.6 points, or 0.05 per cent, to 8,824.6.
At the weekend, the US president posted on social media that he would impose 30 per cent tariffs on the European Union and Mexico from August 1 - but leaders of the EU and Mexico said they would keep negotiating with Mr Trump, so the threat might be a negotiating tactic.
At midday, five of the ASX's 11 sectors were higher and six were lower.
The materials sector was the biggest mover, gaining 0.7 per cent.
BHP had gained 1.3 per cent and Rio Tinto had added 1.1 per cent while Fortescue dipped 0.3 per cent.
Golmdiners were higher as the yellow metal traded at a three-week high of $US3,373 an ounce.
Northern Star had gained 1.5 per cent, Evolution was up 1.0 per cent and Vault Minerals had advanced 2.6 per cent.
Rare earth miner Pilbara had climbed 5.3 per cent to an almost four-month high of $1.6325 following the Pentagon's decision last week to take a billion-dollar stake in a US rare earth miner.
In the financial sector, NAB was up 0.1 per cent but the other three big banks were lower.
CBA and Westpac had dropped 0.7 per cent and ANZ had slid 0.8 per cent.
Elsewhere, Droneshield had gained 7.4 per cent to an all-time high of $2.975 after the military contractor said it would spend $13 million to build a new production facility in the Sydney suburb of Alexandria to meet high demand for its anti-drone products.
Hansen Technologies was up 11.5 per cent to a two-month high of $5.33 after the software provider to the energy and utility companies upgraded guidance, citing disciplined cost management.
Abacus Storage King had gained 5.9 per cent to $1.5625 after the self-storage giant said a consortium looking to acquire it had lifted its tentative takeover offer by almost 15 per cent, to $2.17 billion.
The offer is being made by New York-listed Public Storage and Ki Corporation, the family office of South African businessman Nathan Kirsh.
The Australian dollar was buying 65.59 US cents, from 65.72 US cents at the close of business on Friday.
Bitcoin had set another all-time high about lunchtime, at $US119,900 ($A181,900).
The original cryptocurrency is up two per cent in the past 24 hours and almost 10 per cent in the past week.
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