China said it would impose levies of 10 and 15 percent on a range of US agricultural imports in response to Trump's tariffs.
The US president signed an executive order to increase a previously imposed 10 percent tariff on Chinese goods to 20 percent, the White House said on Monday.
US tariffs also came into effect on imports from major trading partners Canada and Mexico after a deadline to avert the levies passed without a deal being struck.
Canada said it would respond in kind, with 25 percent tariffs on $155 billion worth of US goods taking effect after the deadline.
Fears of a full-blown trade war increased volatility with Asian markets mostly lower.
Tokyo recovered some of its early losses to end down 1.2 percent after China announced its retaliatory tariffs.
Japanese automakers with Mexican factories in their supply chains suffered the biggest hit, with Nissan, Toyota and Honda among the major losers.
Hong Kong closed in the red after a volatile session with Singapore, Bangkok, Sydney, Wellington, Taipei, Jakarta, Kuala Lumpur and Seoul also down. Manila and Shanghai were the only gainers.
Concerns over the impact of a tariff war spread to European markets, with London, Paris and Frankfurt all opening lower.
"The spectre of a full-blown trade war is once again looming, threatening to choke global economic growth just as investors were starting to regain confidence," said Stephen Innes of SPI Asset Management.
Investors are hoping that China will announce a huge economic stimulus package at its key parliamentary meeting, the National People's Congress, which opens Wednesday.
"In the upcoming National People's Congress, Chinese policymakers could provide more pro-growth measures including announcing a larger budget deficit target and maintaining a five percent growth target for this year," said MUFG Bank's Lloyd Chan.
Both the Mexican peso and Canadian dollar have dropped against the greenback over the past few days.
Trump expressed outrage on Monday over the weakening of certain currencies, accusing Beijing and Tokyo of using it as a trade strategy, although the Japanese government fiercely refuted the claim.
The oil market also saw sharp declines, with West Texas Intermediate crude falling to $67.60 per barrel and Brent crude dropping to $70.66 per barrel.
Bitcoin's price plunged nearly 10 percent on Monday as concerns of an escalating trade war pushed investors to seek safer investments.
Bitcoin and similar digital assets had surged at the weekend after Trump suggested creating a national cryptocurrency reserve.
"Everything is getting sold," Forexlive manager Adam Button said. "There's a de-risking that's unfolding" among crypto investors, he said.
- Key figures around 0815 GMT -
Tokyo - Nikkei 225: DOWN 1.2 percent at 37,331.18 (close)
Hong Kong - Hang Seng Index: DOWN 0.3 percent at 22,941.77 (close)
Shanghai - Composite: UP 0.2 percent at 3,324.21 (close)
London - FTSE 100: DOWN 0.5 percent at 8,821.65
Euro/dollar: UP at 1.0517 from $1.0419 on Monday
Pound/dollar: UP at $1.2719 from $1.2612
Dollar/yen: DOWN 149.16 from 150.28 yen
Euro/pound: UP at 82.69 pence from 82.62 pence
West Texas Intermediate: DOWN 1.13 percent at $67.60 per barrel
Brent North Sea Crude: DOWN 1.34 percent at $70.66 per barrel
New York - Dow: DOWN 1.5 percent at 43,191.24 (close)
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