The Tokyo Stock Exchange's Nikkei 225 index was down 2.8 percent, while the broader Topix index pointed to a minus 1.9 percent at lunch local time.
At the same time, Hong Kong's Hang Seng pointed to a minus 2.2 percent. Shanghai and Shenzhen's composite index were down 0.9 and 1.6 percent, respectively, and South Korea's Kospi index had plummeted 3.2 percent.
Trump announced on Thursday that the US's 25 percent tariffs on Canada and Mexico will become a reality as of March 4. Furthermore, China will receive an additional 10 percent surcharge, on top of the 10 percent increase that came into effect earlier in February, according to the president.
Since both China and Mexico and Canada have also threatened countermeasures, the market's fear of a full-scale trade war is increasing – and for rising inflation in the US in its wake. The uncertainty contributed to the indexes on Wall Street also falling in Thursday's trading, with the technology-heavy Nasdaq composite index retreating 2.8 percent.
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