The US president's outburst came after a series of announcements last week including warnings of 50 percent levies on copper and Brazilian goods, 35 percent on Canadian goods, and a possible 200 percent charge on pharmaceuticals.
While observers warn the measures could deal a hefty blow to the global economy, investors are largely optimistic that governments will hammer out agreements before the White House's August 1 deadline.
In announcing his latest measures on Saturday, Trump cited Mexico's role in illicit drugs flowing into the United States and a trade imbalance with the European Union.
The move threw months of painstaking talks with Brussels into disarray.
European Commission chief Ursula von der Leyen has insisted the bloc still wants to reach an accord -- and on Sunday delayed retaliation over separate US duties on steel and aluminium as a sign of goodwill.
EU officials threatened in May to impose tariffs on US goods worth around 100 billion euros ($117 billion), including cars and planes, if talks fail.
The bloc's trade chief Maros Sefcovic said he planned to speak to his US counterparts Monday, adding that he "cannot imagine walking away without genuine effort".
French President Emmanuel Macron backed efforts to reach an agreement that "reflects the respect that trade partners such as the European Union and the United States owe each other".
But he urged the bloc to "step up the preparation of credible countermeasures" if the two sides fail to reach an agreement.
Analysts also pointed out that the levies against Mexico and Canada come even after Trump agreed a trade deal with the two during his first administration.
Shares fell in Frankfurt and Paris, though London ticked higher.
In Asia, Hong Kong, Shanghai, Seoul, Singapore, Manila, Bangkok and Jakarta all rose, while Tokyo, Sydney, Taipei, Mumbai and Wellington edged down.
Bitcoin hit a new record high of $123,205.
"It is hard to say whether the muted market response over the week is best characterised by resilience or complacency," said National Australia Bank's Taylor Nugent.
"But it is difficult to price the array of headlines purportedly defining where tariffs will sit from 1 August when negotiations are ongoing."
Data showed Chinese exports jumped more than expected in June after Washington and Beijing agreed a tentative deal to lower swingeing levies on each other.
That included a 32.4 percent surge in shipments to the United States, having dropped in May.
Traders are also keeping a nervous eye on the Federal Reserve as Trump continues to berate boss Jerome Powell for not cutting interest rates soon enough, saying Sunday "I hope he quits", and adding "He should quit".
Reports also said the president's allies were targeting the Fed chief over his handling of an expensive renovation at the bank's headquarters, with some suggesting they were building a case to have him removed over it.
However, strategists warned that such a move would bring the independence of the central bank into question and send US Treasury yields soaring and the dollar plunging.
- Key figures at around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.3 percent at 39,459.62 (close)
Hong Kong - Hang Seng Index: UP 0.3 percent at 24,203.32 (close)
Shanghai - Composite: UP 0.3 percent at 3,519.65 (close)
London - FTSE 100: UP 0.2 percent at 8,961.25
Euro/dollar: DOWN at $1.1685 from $1.1690 on Thursday
Pound/dollar: DOWN at $1.3484 from $1.3497
Dollar/yen: DOWN at 147.36 yen from 147.38 yen
Euro/pound: UP at 86.61 pence from 86.59 pence
West Texas Intermediate: UP 1.2 percent at $69.29 per barrel
Brent North Sea Crude: UP 1.2 percent at $71.18 per barrel
New York - Dow: DOWN 0.6 percent at 44,371.51 (close)
dan/mtp
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