Eyes were also on the release of closely watched US jobs data at the end of the week after the Federal Reserve scaled back its interest rate cut expectations and took a more hawkish turn.
After a tepid start to the week, Asian investors fought to recover on Tuesday after a tech-fuelled rally in the S&P and Nasdaq -- with Nvidia hitting a record -- as strong results from Taiwan-based chip giant Foxconn sparked a fresh rush for semiconductors.
The US gains were also helped after The Washington Post said Trump's aides were weighing plans to apply tariffs only to goods in certain critical sectors -- a more narrow definition than the president-elect previously proposed.
The report comes after Trump warned last year that he would slam huge levies on China, Canada and Mexico amid fears of a return to his hardball trade policy.
However, he later hit back at the Post story, saying it "incorrectly states that my tariff policy will be pared back. That is wrong". He added that it was "just another example of Fake News".
Most markets rose in early Asian business, with Tokyo up two percent helped by a weak yen, while Shanghai, Sydney, Singapore, Seoul, Taipei, Mumbai, Bangkok and Jakarta were also higher. Wellington and Manila fell.
Hong Kong also retreated as tech firms took a hit with Tencent diving more than seven percent after it was named by the United States in a list of "Chinese military companies". Its US-listed shares shed 7.8 percent.
A spokesperson for Tencent said the company's inclusion on the list "is clearly a mistake", and that "we are not a military company or supplier".
Still, Morningstar senior equity analyst Ivan Su said: "Given Tencent's business model -—which primarily revolves around social networking and online gaming -- we believe the company has a good chance to secure exclusion through US courts."
Major battery manufacturer CATL, which was also named on the list, sank 5.2 percent in Shenzhen before paring the losses.
The announcement came just weeks before Trump returns to the White House, with many commentators fearing another trade war with China.
There is also growing concern that his plans to slash taxes, remove regulations, impose tariffs on imports and crack down on immigration will reignite inflation, putting pressure on the Fed to keep borrowing costs higher for longer.
"While an aggressive Trump may try to deliver large fiscal stimulus, stronger demand would quickly run into a deteriorating supply side of the US economy," said David Rees, senior emerging markets economist at Schroders.
"Despite being partially absorbed by the stronger US dollar and profit margins, substantially higher tariffs would be likely to increase goods inflation.
"But the greater threat to inflation probably comes from a crackdown on immigration, along with mass deportations, if it leads to labour shortages that would ultimately result in higher wages and services inflation."
Friday's non-farm payroll report is the next big marker for investors hoping for some idea about the Fed's plans for rates after it scaled back its forecasts for cuts in 2025 last month.
Key figures around 0710 GMT
Tokyo - Nikkei 225: UP 2.0 percent at 40,083.30 (close)
Hong Kong - Hang Seng Index: DOWN 1.8 percent at 19,335.05
Shanghai - Composite: UP 0.7 percent at 3,229.64 (close)
Euro/dollar: UP at $1.0400 from $1.0388 on Monday
Pound/dollar: UP at $1.2539 from $1.2518
Dollar/yen: UP at 157.76 yen from 157.64 yen
Euro/pound: DOWN at 82.92 pence from 82.98 pence
West Texas Intermediate: DOWN 0.2 percent at $73.41 per barrel
Brent North Sea Crude: DOWN 0.1 percent at $76.20 per barrel
New York - Dow: DOWN 0.1 percent at 42,706.56 (close)
London - FTSE 100: UP 0.3 percent at 8,249.66 (close)
