The benchmark S&P/ASX200 on Tuesday dropped 58.2 points, or 0.69 per cent, to 8,359.4, while the broader All Ordinaries fell 48.6 points, or 0.56 per cent, to 8,612.6.
Overnight on Truth Social, Mr Trump said one of his first acts as president when he takes office on January 20 would be to impose 25 per cent tariff on all goods coming in from Mexico and Canada.
"This Tariff will remain in effect until such time as Drugs, in particular Fentanyl, and all Illegal Aliens stop this Invasion of our Country!" Mr Trump wrote.
He promised additional 10 per cent tariffs on China because of what he described as "the massive amounts" of Chinese-made fentanyl pouring into the US.
IG analyst Tony Sycamore saw the announcement as risk-positive, however, pointing out a 10 per cent increase on tariffs on China would place the average tariff on that country at 27 per cent - considerably lower than the 60 per cent fee Mr Trump threatened during his campaign.
Also on Tuesday, the big four banks all finished lower after the Australian Prudential Regulation Authority on Monday said it would leave the mortgage serviceability buffer unchanged, meaning banks will still have to assess mortgage applications as if interest rates are three percentage points higher than current levels.
There have been calls to drop the buffer given how much interest rates have risen since 2022.
CBA dropped 3.6 per cent to $154.46, NAB dipped 1.2 per cent to $39.14, Westpac fell 1.4 per cent to $32.95 and ANZ retreated 1.7 per cent to $31.30.
Overall five of the ASX's 11 sectors finished higher and five finished lower, with utilities basically flat.
Energy was the biggest mover, dropping 3.1 per cent as Brent crude traded at a five-day low of $73 a barrel on signs of an Israel-Hezbollah ceasefire.
Woodside fell 3.8 per cent, Santos subtracted 4.2 per cent and Beach Energy fell 4.3 per cent.
The easing risk of all-out war in the Middle East was seen as behind a decline in the price of gold, with the safe-haven asset changing hands at a one-week low of $US2,621 an ounce, leading to falls for goldminers.
Northern Star and Evolution both dropped 2.4 per cent, while Newmont dipped 0.5 per cent and Vault Minerals declined 4.4 per cent.
Elsewhere in the materials/mining sector, BHP dropped 0.9 per cent to $39.86, Fortescue fell 0.4 per cent to $18.30 while Rio Tinto grew 0.3 per cent to $117.10.
Bluescope Steel, which has US operations and could potentially benefit from US tariffs, climbed 5.6 per cent to $22.43.
Plumbing supply company Reece and shipbuilder Austal, which also have US operations, rose 2.2 per cent and 1.6 per cent respectively.
In tech, Gentrack Group soared 28.1 per cent to an all-time high of $12.04 after the Kiwi software provider for utilities and airports said its full-year revenue was up 25.5 per cent to $NZ213.2 million after new customer wins and strong demand for its services.
The Australian dollar was buying 64.89 US cents, from 65.15 US cents at Monday's ASX close.
On Wednesday the Australian Bureau of Statistics will release October consumer price data, a readout that will be scrutinised because of the impact waning inflation will have on the timing and pace of interest rate cuts next year.
ON THE ASX:
* The benchmark S&P/ASX200 index finished Tuesday down 58.2 points, or 0.69 per cent, at 8,359.4
* The broader All Ordinaries dropped 48.6 points, or 0.56 per cent, to 8,612.6
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 64.89 US cents, from 65.15 US cents at Monday's ASX close
* 99.81 Japanese yen, from 100.63 Japanese yen
* 61.96 euro cents, from 62.20 euro cents
* 51.73 British pence, from 51.75 pence
* 111.12 NZ cents, from 111.34 NZ cents.
