A surge in tech giants including Tesla and Nvidia helped New York markets higher, with sentiment buoyed by indications from the White House that next week's glut of levies would be less severe than feared.
Trump has dubbed April 2 "Liberation Day" as he pledges to impose reciprocal tariffs on trading partners in an effort to remedy practices that Washington deems unfair.
Since resuming office in January, Trump has pursued a hardball policy approach, taking aim at friend and foe alike, sending shivers through markets and fanning fears about the global economy.
In recent days, he has suggested some countries could be given exemptions or reductions from next week's measures, giving investors a much-needed sense of optimism.
Market-watchers say the final outcome would likely see the tariffs changed after negotiations.
"The recent wave of doom-laced narratives -- fuelled by politically skewed consumer sentiment surveys and a flood of bearish op-eds -- looks increasingly overcooked," said SPI Asset Management's Stephen Innes.
And IG market analyst Tony Sycamore added: "The expectation is that the process will be more organised and structured than previous actions. Whatever numbers are announced on 2 April are likely to be negotiated down from there."
Still, the president did provide a jolt by warning countries that bought crude and gas from Venezuela would face steep tariffs, a move that could hit China and India among others.
In early trade, Tokyo, Sydney, Singapore, Taipei and Wellington rose but Shanghai and Manila dropped.
Hong Kong sank more than one percent, weighed by a drop of almost five percent in Chinese tech giant Xiaomi after it raised $5.5 billion in a mega share sale as it looked to expand its electric vehicle business.
Seoul also fell, despite a surge of around six percent in South Korean automaker Hyundai following news of a $21 billion US investment.
Eyes are also on the release this week of US personal consumption expenditure data, which is the Federal Reserve favoured inflation metric.
The reading will be closely monitored amid warnings that prices will likely go up because of Trump's tariffs.
Atlanta Fed chief Raphael Bostic said the measures would likely mean the bank cuts interest rates just once this year.
"I moved to one mainly because I think we're going to see inflation be very bumpy and not move dramatically and in a clear way to the (Fed's) two percent target," he told Bloomberg Television on Monday.
"Because that's being pushed back, I think the appropriate path for policy is also going to have to be pushed back."
Oil prices held Monday's gains of more than one percent that came in response to Trump's warning on Venezuelan crude.
- Key figures around 0230 GMT -
Tokyo - Nikkei 225: UP 0.7 percent at 37,881.70 (break)
Hong Kong - Hang Seng Index: DOWN 1.7 percent at 23,502.90
Shanghai - Composite: DOWN 0.1 percent at 3,367.17
Euro/dollar: DOWN at $1.0799 from $1.0805 on Monday
Pound/dollar: DOWN at $1.2917 from $1.2924
Dollar/yen: UP at 150.64 yen from 150.58 yen
Euro/pound: UP at 83.61 pence from 83.58 pence
West Texas Intermediate: FLAT at $69.09 per barrel
Brent North Sea Crude: FLAT at $72.37 per barrel
New York - Dow: UP 1.4 percent at 42,583.32 points (close)
London - FTSE 100: DOWN 0.1 percent at 8,638.01 (close)
dan/lb
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