The initial 10 per cent "baseline" tariff to be paid by US importers took effect at US seaports, airports and customs warehouses on Saturday.
"This is the single biggest trade action of our lifetime," said Kelly Ann Shaw, a trade lawyer at Hogan Lovells and former White House trade adviser during Trump's first term.
Shaw told a Brookings Institution event on Thursday that she expected the tariffs to evolve over time as countries seek to negotiate lower rates.
"But this is huge. This is a pretty seismic and significant shift in the way that we trade with every country on earth," she added.
Trump's Wednesday tariff announcement shook global stock markets.
Prices for oil and commodities plunged while investors fled to the safety of government bonds.
Among the countries first hit with the 10 per cent tariff are Australia, the United Kingdom, Colombia, Argentina, Egypt and Saudi Arabia.
A US Customs and Border Protection bulletin to shippers indicates no grace period for cargoes on the water at midnight on Saturday.
But a US Customs and Border Protection bulletin did provide a 51-day grace period for cargoes loaded onto vessels or planes and in transit to the US before 12.01am ET on Saturday.
These cargoes need to arrive by 12.01am ET on May 27 to avoid the 10 per cent duty.
Trump's higher "reciprocal" tariff rates of 11 per cent to 50 per cent are due to take effect on Wednesday.
European Union imports will be hit with a 20 per cent tariff while Chinese goods will be hit with a 34 per cent tariff, bringing Trump's total new levies on China to 54 per cent.
China on Saturday said "the market has spoken" in rejecting Trump's tariffs after it hit the US with a slew of countermeasures, including extra levies of 34 per cent on all US goods and export curbs on some rare earth minerals.
"China has been hit much harder than the USA, not even close," Trump said on Saturday on social media.
"THIS IS AN ECONOMIC REVOLUTION, AND WE WILL WIN. HANG TOUGH, it won't be easy, but the end result will be historic."
Shortly after posting the comment, Trump was spotted arriving at his Trump National Golf Club in Jupiter, Florida, reading a New York Post article covering China's retaliation to Trump's tariffs and the stock market fall.
"A trade war is in no one's interest. We must stand united and resolute to protect our citizens and our businesses," French President Emmanuel Macron said in post on X.
Some world leaders moved quickly to strike a deal with Trump to avert economic disruption while others weighed countermeasures.
Israeli Prime Minister Benjamin Netanyahu is expected to visit the White House on Monday as unspecified goods from the country face a 17 per cent tariff under the new policy.
Japanese Prime Minister Shigeru Ishiba was reportedly seeking a telephone conversation with Trump.
Japan faces a 24 per cent levy.
Vietnam, which benefited from the shift of US supply chains away from China after Trump's first-term trade war with China, will be hit with a 46 per cent tariff and agreed on Friday to discuss a deal with Trump.
Italian Economy Minister Giancarlo Giorgetti warned on Saturday against the imposition of retaliatory tariffs on the United States, saying at a business forum near Milan that doing so could cause damage.
Elon Musk, a close Trump adviser, told a political event in Italy by video on Saturday that he hoped to see complete freedom of trade between the United States and Europe, which he described as "a zero tariff situation".
Canada and Mexico were exempt from Trump's latest duties but still face a 25 per cent tariff imposed recently on goods that do not comply with rules of origin under a North America trade accord.
While Trump's order exempted 1000 product categories from the new tariffs such as pharmaceuticals, uranium and semiconductors, the administration is considering new duties on some of them.
Trump is excluding goods subject to separate, 25 per cent national security tariffs, including steel and aluminium, cars, trucks and car parts.
His administration also released a list of more than 1000 product categories exempted from the tariffs.
Valued at $US645 billion ($A1.1 trillion) in 2024 imports, these include crude oil, petroleum products and other energy imports, pharmaceuticals, uranium, titanium, lumber and semiconductors and copper.
Except for energy, the Trump administration is investigating several of these sectors for further national security tariffs.
