Japan's Nikkei and Hong Kong's Hang Seng saw the biggest drop, tumbling more than two percent and 1.5 percent respectively.

It comes after the White House said Trump had signed on Monday an executive order to increase a previously imposed 10 percent tariff on China, to 20 percent.

The US president also stressed that Canada and Mexico would not avoid being hit with 25 percent levies, causing US stocks to fall on Monday.

Canada responded on Tuesday by putting 25 percent tariffs against $155 billion worth of American goods.

Beijing also warned on Tuesday that it would take countermeasures against new US tariffs on Chinese imports.

"China is strongly dissatisfied with this and firmly opposes it, and will take countermeasures to resolutely safeguard its own rights and interests," a commerce ministry spokesperson said in a statement.

Fears the retaliatory tariffs could escalate into a full-blown trade war, drove markets down across Asia on Tuesday.

Japanese automakers with Mexican factories in their supply chain suffered, with Nissan (-2.11%), Toyota (-2.25%), or Honda (-2.12%) among the major losers.

Exchanges across Asia mirrored the downward trajectory, with Thailand, Australia, New Zealand and Taiwan dropping around one percent.

South Korea, the Philippines and Malaysia also fell.

"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, SPI Asset Management.

Investors are hoping China will announce a huge stimulus package at its key parliamentary meeting on Wednesday, the National People's Congress, to stimulate the economy.

"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 Lloyd Chan, from MUFG bank.

Trump expressed outrage on Monday over the weakening of certain currencies and accused Beijing and Tokyo of using it as a trade strategy - a claim fiercely refuted by the Japanese government.

The oil market also saw sharp declines with US WTI crude oil falling 0.54 percent to $68 per barrel, and Brent crude from the North Sea dropping 0.77 percent to $71.06 per barrel at around 0200 GMT.

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 over the weekend after Trump suggested creating a national cryptocurrency reserve.

"Everything is getting sold," Forexlive manager Adam Button said, adding: "There's a de-risking that's unfolding" among crypto investors.

- Key figures around 0230 GMT -

Tokyo - Nikkei 225: DOWN 1.84 percent at 37,090.72 (break)

Hong Kong - Hang Seng Index: DOWN 1.3 percent at 22,706.40

Shanghai - Composite: DOWN 0.2 percent at 3,310.14

Euro/dollar: UP at 1.0485 from $1.0419 on Monday

Pound/dollar: UP at $1.2694 from $1.2612

Dollar/yen: DOWN 149.32 from 150.28 yen

Euro/pound: DOWN at 82.60 pence from 82.62 pence

West Texas Intermediate: DOWN 0.42 percent at $68.08 per barrel

Brent North Sea Crude: DOWN 0.66 percent at $71.15 per barrel

New York - Dow: UP 1.4 percent at 43,840.91 (close)

London - FTSE 100: UP 0.6 percent at 8,809.74 (close)