The losses followed a broadly negative day in New York, where tech giants have hit a wall since China's DeepSeek unveiled a chatbot that upended the AI industry and led traders to reassess their recent vast investments.
They also come ahead of the release of earnings from market darling Nvidia, which will be closely watched for its views on the outlook in light of the Chinese startup's arrival.
After a healthy run in February, markets have been put on the back foot since Trump said on Monday that he plans to proceed with tariffs on Canada and Mexico once a 30-day suspension expires next week.
Levies were announced against countries in January but Trump said they would be delayed by a month to allow for negotiations. Tariffs on Chinese goods went ahead without a grace period.
The comments came after Mexican President Claudia Sheinbaum said earlier in the day that talks would continue this week to avoid the sweeping levies.
Asked about a Bloomberg News report that the United States was pushing her government to impose duties on Chinese imports, Sheinbaum said it was important to "prioritise those places where you have trade agreements versus others where you do not have them".
Canada's Foreign Minister Melanie Joly warned "the threat of tariffs is a real one, and may continue for a while".
Trump's announcement came after he signed a memo at the weekend calling for curbs on Chinese investments in industries including technology and critical infrastructure, healthcare and energy.
The memo called for the Committee on Foreign Investment in the United States (CFIUS) to be used to restrict Chinese stakeholdings.
The move was aimed at promoting foreign investment in the United States, while protecting national security interests "particularly from threats posed by foreign adversaries" like China, the White House said.
The memo singled out China for "increasingly exploiting United States capital to develop and modernise its military, intelligence, and other security apparatuses".
China said the "US approach unduly broadens the concept of national security, and is discriminatory".
The developments fanned tensions between the world's top economic superpowers and added to concerns about the possibility of another debilitating trade war amid growing uncertainty about the global outlook.
"We see market volatility continuing in Hong Kong and China as investors digest the latest news on the Trump investment curbs," said Heron Lim at Moody's Analytics.
However, he added that Trump had been pushing such measures in his first term. Therefore, "Beijing has had some time to mitigate the worst of the damage", Lim added.
"In some sense, the ongoing industrial and R&D policies of China are aimed towards self-reliance. The fact that the stock market in Hong Kong -- seen as the barometer of foreign investor trust in China -- is a long time away from its pre-pandemic peak tells us that these measures are largely priced into investors' valuation of Chinese firms."
Hong Kong, where tech titans including Alibaba and Tencent have led the market to a three-year high, was among the biggest losers.
The Hang Seng Index dropped more than one percent, with Alibaba and ecommerce rival JD.com off more than three percent and Tencent losing nearly three percent.
Alibaba's New York-listed stock sank more than 10 percent Monday.
Shanghai, Tokyo, Sydney, Wellington, Taipei, Manila, Bangkok, Singapore and Jakarta were also in the red.
Seoul retreated as the South Korean central bank cut its economic growth outlook and lowered interest rates amid fears over the impact of Trump's tariff drive and the fallout from President Yoon Suk Yeol's brief declaration of martial law in December.
- Key figures around 0700 GMT -
Tokyo - Nikkei 225: DOWN 1.4 percent at 38,237.79 (close)
Hong Kong - Hang Seng Index: DOWN 1.3 percent at 23,048.41
Shanghai - Composite: DOWN 0.8 percent at 3,346.04 (close)
Euro/dollar: UP at $1.0475 from $1.0468 on Monday
Pound/dollar: UP at $1.2631 from $1.2623
Dollar/yen: UP at 149.78 from 149.76 yen
Euro/pound: UP at 82.93 pence from 82.91 pence
West Texas Intermediate: UP 0.5 percent at $71.06 per barrel
Brent North Sea Crude: UP 0.4 percent at $75.09 per barrel
New York - Dow: UP 0.1 percent at 43,461.21 (close)
London - FTSE 100: FLAT at 8,658.98 (close)
dan/pbt
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