In the NY stock market, the Dow Jones Industrial Average on Monday plunged two-point-38 percent to close at 25-thousand-324-point-99.
China will hike tariffs on $60 billion worth of US imports, starting on June 1.
Items affected include beef, lamb and pork products, as well as various varieties of vegetables, fruit juice, cooking oil, tea and coffee.
Uber has begun trading as a public company just as the USA and China have stepped up the level of trade tariffs.
Trade bellwether Caterpillar fell 4.6% while Apple dropped 5.8%.
"A clear hardening of attitudes, with state media blaring that China 'will fight to the end, ' has stirred concerns of a protracted and widening trade war", Mizuho Bank said in a commentary.
Overseas markets also fell. The Nasdaq Composite, which lost the most in the decline, has climbed almost 1.5%.
The benchmark S&P/ASX200 index was down 44.3 points, or 0.71 per cent, to 6,284.2 points at 1630 AEST on Tuesday.
"Volatility is going to persist". "We're going to be meeting, as you know, at the G20 in Japan and that'll be, I think, probably a very fruitful meeting". But "this is more of a re-evaluation of stocks than it is a pure panic".
On Tuesday, at least, such worries eased.
Treasuries pared gains after the two-year yield touched the lowest level since February 2018, while the 10-year rate traded around 2.38%. The gains at Dow Hones were bolstered by Visa and Boeing shares and the 30-stock index got the best day on Tuesday since April 12. Trump also said that China had a "great deal" nearly completed but they "backed out".
Alec Young, managing director of global markets research at FTSE Russell, said investors are increasingly anxious an anticipated second-half profit rebound may now evaporate as Trump's threat to tariff the remaining $325 billion in Chinese imports will disproportionately target consumer products like iPhones, "thereby posing a greater threat to the consumption-driven USA economy".
That good feeling ended the first week of May, when President Trump tweeted that he would raise tariffs on Chinese goods coming into the USA from 10 percent to 25 percent.
The S&P 500 rose 22.54 points, or 0.8%, to 2,834.41.
Asian stocks "could be in for an extended period of pain", said Jeffrey Halley, senior market analyst at Oanda.
But "an accompanying "reinversion" of the Treasury yield curve suggests that the best days for US equities may be over even if the two economies eventually resolve their dispute".
"J.P. Morgan told its clients to prepare for the worst saying, "... the remaining hurdles are critical and hard.
Some of those losses were mitigated on Friday after stocks staged a massive comeback, however.
The Trump administration is preparing to expand tariffs to a further $300 billion of Chinese goods, although the president hasn't ruled out a trade deal and plans to meet his Chinese counterpart at next month's G-20 summit. Plus, there could be more retaliation from China - last time farmers took a big hit.
Gold fell 0.3% to $1,297.70 an ounce.
However, while there is a lot of fear about an all-out trade war, which could batter the world economy, both said talks will continue, though no date has been set for the next round.
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