The benchmark S&P/ASX200 index at midday on Friday was up 32.5 points, or 0.39 per cent, to 8,411.2, while the broader All Ordinaries had gained 28.8 points, or 0.33 per cent, to 8,657.9.
For the week the ASX was on track for a 1.2 per cent rise, its third straight week of gains and its best weekly performance so far this year.
Overnight Mr Trump made a blustering online address to the World Economic Forum in Davos, calling on Saudi Arabia and the Opec oil producer cartel to cut the cost of oil to choke off revenue to Russia and stop its war against Ukraine.
"You gotta bring the oil price down, that will end that war," he said.
"With oil prices going down, I'll demand that interest rates drop immediately, and likewise they should be dropping all over the world,," Mr Trump added.
At the White House following the event, Mr Trump said he knows interest rates "much better than they do ... certainly much better than the one who's primarily in charge of making that decision," an apparent reference to Federal Reserve chairman Jerome Powell, whom Trump appointed to the US central bank during his first administration.
Despite Mr Trump's pressure, the Fed is widely expected to leave interest rates unchanged at its first policy meeting of 2025 next week.
Brent crude did fall 0.9 per cent to a two-week low of $US78 a barrel following Mr Trump's remarks, although the dip is likely to be transitory unless the Opec cartel follows through with an increase in production.
Nine of the ASX's 11 sectors were higher at midday, all except materials/mining and energy.
The consumer discretionary sector was the biggest gainer, rising 1.7 per cent as Wesfarmers grew 3.0 per cent to a more than one-month high of $US74.48.
Kogan.com had dropped 12.5 per cent to a six-week low of $5.23 after the online retailer reported implementation and technology challenges had adversely impacted sales and profitability of its Mighty Ape business during the peak holiday trading period.
In the heavyweight mining sector, goldminers were generally lower even as the precious metal traded for $US2,768 an ounce - not far from the all-time high of $US2,790 set in October.
Northern Star was down 1.0 per cent, Evolution had slipped 2.2 per cent and Westgold had fallen 5.6 per cent.
Elsewhere in the sector, BHP was up 0.2 per cent, Fortescue had added 0.6 per cent and Rio Tinto was basically flat.
All of the big four banks were higher, with CBA and NAB up 0.6 per cent and Westpac and ANZ up 0.3 per cent.
The energy sector was down 1.0 per cent amid the drop in oil prices, with Woodside falling 1.4 per cent, Santos dipping 0.4 per cent and Ampol retreating 1.0 per cent.
The Australian dollar meanwhile had moved back above 63 US cents for the first time since mid-December, when the US Federal Reserve indicated that it would likely cut interest rates in 2025 more slowly than previously forecast.
This caused a sell-off in the share market and the greenback to strengthen against other currencies.
The Aussie was buying 63.01 US cents, from 62.72 US cents at Thursday's ASX close.
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