The Dow Jones Industrial Average and S&P 500 index each fell more than 2 per cent as investors sold trade-sensitive shares.
Bank stocks also fell sharply.
Tariffs on Chinese goods increased from 10% to 25% on Friday, making the underlying cost of those items higher for US customers.
On Twitter, Trump warned Xi that China "will be hurt very badly" if it doesn't agree to a trade deal. Trump wrote that Beijing "had a great deal, nearly completed, & you backed out!" And in terms of its economic impacts, it's the total trade deficit that matters, not the balance with individual countries.
China imports almost half of the world's copper, and the country's economic growth had been slowing well before the trade dispute began to impact the outlook for industrial metals. To date, tariffs have largely affected raw materials like chemicals and wooden beams used to make other products, so the cost increases appear incremental to the consumer. China responded by upping tariffs on $60 billion of US goods.
Speaking several hours later at a dinner gathering at the White House, Trump said it should be clear in "three or four weeks" if a US trade delegation's trip to Beijing two weeks ago was successful. But nothing has been scheduled. Kudlow also said that Trump and Chinese President Xi Jinping may meet in late June at the G-20 summit in Japan.
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On Tuesday, the president remained defiant, tweeting: "In one year Tariffs have rebuilt our Steel Industry - it is booming!"
He downplayed concerns that the tariffs would lead to USA job losses and hurt the GDP. That has "led to an escalation of Sino-U.S. economic and trade frictions", the finance ministry said, adding that U.S. actions "jeopardize the interests of both sides".
Mr. Trump said the two countries are trying to smooth out their differences, after negotiations collapsed last week, but insisted the US will "always win".
"What that means for soybean growers is that we're losing", Davie Stephens, president of the American Soybean Association, said in a statement. "Losing a valuable market, losing stable pricing, losing an opportunity to support our families and our communities". Remember, they broke the deal with us and tried to renegotiate. The yield on the 10-year Treasury fell to 2.40 per cent from 2.45per cent late Friday. "Therefore, China should not retaliate-will only get worse!"
"We're having a little squabble with China", he said. "You can't move these goalposts like they're moving them and expect to be respected".
Trump started raising tariffs last July over complaints China steals or pressures companies to hand over technology.
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In a Tuesday morning discussion with reporters, Portman said he supports getting tough on China because it has stolen US intellectual property and technology and has a huge trade imbalance that the United States needs to address.
Trump later tweeted that "there will be nobody left in China to do business with".
The best example of why that is, according to Hufbauer, is the 25% tariff that has long protected light trucks in the US from foreign competition.
The tensions "raise fresh doubts about this recovery path", said Morgan Stanley economists in a report.
The latest US list of 3,805 product categories is a step toward carrying out Trump's May 5 threat to extend punitive 25 percent duties to all Chinese imports, the USTR said. That would pull annual growth below 6%, raising the risk of politically risky job losses.
"There is nothing to be afraid of", said the party newspaper People's Daily. But it remains hopeful "that the US can work together with China, moving in the same direction, to resolve each other's legitimate concerns on the basis of mutual respect and equality".
"It's no big deal".
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"We've never taken in ten cents [in tariffs] until I got elected", Trump told reporters Monday from the Oval Office.