Greater China markets recorded heavy losses on the back of that news. On the mainland, the fell 3.82 percent to close below the 3,000 mark at 2,906.43. The smaller Shenzhen composite sank 5.77 percent and closed at 1,594.05.

In turn, China said it would take countermeasures if the U.S. went ahead with the additional tariffs it had threatened.

Trump said on Monday that he had asked the U.S. Trade Representative to identify $200 billion worth of Chinese products that will be subject to additional tariffs of 10 percent. Those tariffs will take effect if China did not "change its practices," Trump added in a statement.

Chinese markets led losses in Asia on Tuesday, with major markets in the region closing sharply lower after U.S. President Donald Trump fired a fresh salvo in the ongoing trade spat between the U.S. and China.

Other Asian markets saw slimmer losses, with Japan's closing down 1.77 percent, or 401.85 points, at 22,278.48 and South Korea's Kospi declining 1.52 percent to end at 2,340.11. Australian stocks finished the day little changed at 6,102.10.

MSCI's broad index of shares in Asia Pacific outside of Japan was down 2.03 percent during Asia afternoon trade.

"The tit for tat brings the two sides closer to a trade war," Louis Kuijs, head of Asia Economics at Oxford Economics, said in a note.

"The Trump administration appears to think it can strong-arm China in making concessions by scaling up the amount of trade it imposes tariffs on. However, China is adamant about not wanting to look weak in this conflict with the US," he added.

Markets elsewhere, meanwhile, looked set to decline. U.S. stock index futures were lower during Asia afternoon trade, with Dow Jones industrial average futures down 374 points. S&P 500 e-mini futures were lower by 1.26 percent.

Safe-haven plays like the Japanese currency firmed as investors turned to lower-risk assets. The yen traded at 109.63 to the dollar at 3:05 p.m. HK/SIN, compared to the 110.5 handle seen during the New York session.

The elevated trade tensions between the U.S. and China have had investors nervous over the trade dispute between the world's two largest economies having an effect on the broader economy.

"The threats will affect stock markets, obviously ... But neither side has actually imposed any significant tariff so it's hard to see this as a trade war. It's more like a financial war," Derek Scissors, Asia economist at American Enterprise Institute, told CNBC's "Street Signs."

Trump's most recent tariff threat came after the U.S. on Friday announced that it would impose a 25 percent tariff on up to $50 billion of Chinese products. Tariffs on an initial list of goods worth some $34 billion will kick in on July 6.

In response, China announced tariffs on the same total value of products, with duties on $34 billion of U.S. goods expected to be implemented in July.

"There is a gradual adjustment taking place in markets—investors have gotten used to the stream of trade-related headlines coming out of the U.S. and are being more judicious in reacting to them," Hannah Anderson, global market strategist at J.P. Morgan Asset Management, said in an email. At the same time, with trade tensions now translating into action, investors were better off exercising a greater degree of discretion, she added.

On the commodities front, oil prices slipped after advancing on Monday. Analysts attributed the last session's gains to reports that oil producers were discussing a smaller-than-expected increase in production.

Output cuts holding back some 1.8 million barrels per day have been in place since 2017 in a bid to prop up prices. Oil exporters, including Saudi Arabia and Russia, will meet in Vienna later this week to discuss those production limits.

Brent crude futures were lower by 0.98 percent at $74.60 per barrel and U.S. crude futures dropped 1.08 percent to trade at $65.14.

Meanwhile, in corporate news, Japan's Fujifilm Holdings sued Xerox on Monday for more than $1 billion after the latter dropped a proposed merger in May. Fujifilm shares fell 1.56 percent.

Elsewhere, shares of ZTE dropped more than 20 percent in Hong Kong by 3:05 p.m. HK/SIN after the U.S. Senate passed a bill that had implications for an agreement struck with the company to allow it to resume doing business with U.S. firms.