The benchmark S&P/ASX200 gained 47.3 points, or 0.57 per cent, to 8,406.7 on Wednesday, while the broader All Ordinaries rose 47 points, or 0.55 per cent, to 8,659.6.
The gains came as analysts assessed that the tariffs that Trump had talked up on social media on Tuesday were unlikely to be imposed, at least on Mexico and Canada.
Instead, they were likely to used as negotiation tools to meet drug enforcement and immigration objectives, Barclays analysts wrote.
In the Middle East, Israel and Hezbollah made progress in ceasefire talks, while New Zealand's central bank cut interest rates by a half a percentage point, as expected.
Closer to home a consumer price index readout showing underlying inflation ticked upward in October seemed to have little impact on the market.
The Australian Bureau of Statistics report indicated the Reserve Bank's preferred metric of inflation, trimmed mean inflation, was 3.5 per cent in October, up from 3.2 per cent in September.
HSBC chief economist Paul Bloxham said the readout reinforced his view that the Reserve Bank would not cut rates until the second quarter of 2025 at the earliest, and he gave a 25 per cent chance the RBA would not trim rates at all in 2025.
Still, every sector of the ASX gained ground on Wednesday, with consumer discretionaries the biggest mover, rising 1.0 per cent.
Web Travel Group soared 13.5 per cent to a six-week high of $4.80 as the business-to-business travel industry platform said it would spend up to $150 million buying back shares.
Flight Centre added 2.6 per cent and Harvey Norman rose 2.3 per cent as the electronics and homewares retailer told its annual general meeting that Australian same-store sales were up 3.1 per cent for the first four months of 2024/25.
All of the big four banks finished higher, with CBA rising 2.0 per cent to $157.57, Westpac adding 0.6 per cent to $33.13, ANZ climbing 0.3 per cent to $31.39 and NAB rising 0.1 per cent to $39.19.
In the heavyweight mining sector, goldminers did well as the precious metal traded at $US2,641 an ounce.
Northern Star rose 2.6 per cent, Evolution climbed 2.0 per cent and Genesis Minerals grew 3.7 per cent.
Elsewhere in the sector, BHP dipped 0.2 per cent to $39.78 while Rio Tinto edged 0.1 per cent higher at $117.18 and Fortescue rose 1.9 per cent to $18.65.
In tech, Life360 rose 6.2 per cent to a record high of $24.70, with the family tracking platform having climbed 17.6 per cent in the past three days.
In communications, Aussie Broadband rose 4.8 per cent to $3.75 after the internet service provider said it would buy back up to 10 per cent of its shares.
The Australian dollar was buying 64.75 US cents, from 64.89 US cents at Tuesday's ASX close.
ON THE ASX:
* The benchmark S&P/ASX200 index finished Wednesday up 47.3 points, or 0.57 per cent, at 8,406.7
* The broader All Ordinaries gained 47 points, or 0.55 per cent, to 8,659.6.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 64.75 US cents, from 64.89 US cents at Tuesday's ASX close
* 98.56 Japanese yen, from 99.81 Japanese yen
* 61.79 euro cents, from 61.96 euro cents
* 51.51 British pence, from 51.73 pence
* 110.34 NZ cents, from 111.12 NZ cents.
