Investor sentiment has been jolted in recent weeks by fears that the president's hardball policies could deal a painful blow to the global economy.
He has caused ructions on trading floors since resuming power in January by hitting out at long-standing allies and imposing or threatening swingeing tariffs on imports of an array of goods, including steel and cars.
Next Wednesday is now the focus of attention, with Trump labelling it "Liberation Day" as he prepares to unveil a raft of reciprocal measures to counter those in other countries.
"Anticipation and pre-positioning ahead of Trump's 'Liberation Day' on 2 April and the impending deluge of tariff-related announcements that will follow in the days/weeks after will be a growing factor that drives price action, sentiment and liquidity in markets this week," said Chris Weston at Pepperstone.
"As the sky begins to bruise and darken, and the atmospheric pressure builds within the capital markets, market players question if it's time to batten down the hatches in preparation for a storm of uncertainty set to be unleashed on markets."
The Federal Reserve last week warned that "uncertainty around the economic outlook has increased" while the central banks of Japan and Britain also warned about the impact of the White House's policies.
Chinese Premier Li Qiang said at the weekend that Beijing was readying for "shocks that exceed expectations" ahead of the latest measures, adding that "instability and uncertainty are on the upswing".
His comments came as he met heads of some of the world's biggest companies, including Apple, Qualcomm, FedEx and Pfizer.
And Australian Treasurer Jim Chalmers told Bloomberg News the moves by Trump "are not surprising, but they are seismic".
However, there was some hope among investors after Bloomberg News reported that the US administration was considering a more targeted approach to the tariffs, with some countries being hit harder than others, and the measures not being as severe as initially feared.
That came after the president told reporters Friday that "there'll be flexibility" in his plans.
Asian markets fluctuated through the day, with Tokyo falling along with Seoul, Taipei, Manila and Bangkok.
Jakarta dived more than four percent at one point, extending a recent sell-off fuelled by worries about Southeast Asia's biggest economy that has seen the country's main index lose around 15 percent since the turn of the year.
Hong Kong rose 0.9 percent after two days of losses, while Shanghai, Sydney, Singapore, Mumbai and Wellington also edged up.
London, Paris and Frankfurt opened on the front foot.
Gold held around $3,025, having hit a series of records last week to a peak of more than $3,057 owing to a surge in demand for safe havens.
- Key figures around 0815 GMT -
Tokyo - Nikkei 225: DOWN 0.2 percent at 37,608.49 (close)
Hong Kong - Hang Seng Index: UP 0.9 percent at 23,905.56 (close)
Shanghai - Composite: UP 0.2 percent at 3,370.03 (close)
London - FTSE 100: UP 0.5 percent at 8,687.34
Euro/dollar: UP at $1.0840 from $1.0815 on Friday
Pound/dollar: UP at $1.2949 from $1.2918
Dollar/yen: UP at 149.64 yen from 149.36 yen
Euro/pound: UP at 83.73 pence from 83.72 pence
West Texas Intermediate: UP 0.3 percent at $68.48 per barrel
Brent North Sea Crude: UP 0.2 percent at $72.33 per barrel
New York - Dow: UP 0.1 percent at 41,985.35 points (close)
dan/mtp
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