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The White House has criticised China after it imposed retaliatory tariffs against the US on a range of goods, including pork and wine.
Beijing put duties of up to 25% on 128 American imports following President Donald Trump's decision to slap taxes on imports of steel and aluminium.
China said the move was intended to safeguard its interests and balance losses caused by the new tariffs.
US stocks fell sharply and Asia traded generally lower, amid trade war fears.
On Wall Street, the S&P 500 Index lost 2.2%, while the Dow Jones Industrial Average dropped 1.9%.
In Asia, Japan's Nikkei 225 opened down about 1.5% on Tuesday but recovered a little to close 0.45% lower. The Shanghai Composite closed down even further, dropping 0.84%, although Hong Kong's Hang Seng bucked the trend, reversing earlier losses to finish up 0.29%.
The White House reacted angrily to China's move.
"Instead of targeting fairly traded US exports, China needs to stop its unfair trading practices which are harming US national security and distorting global markets," spokeswoman Lindsay Walters said.
She added; "China's subsidisation and continued overcapacity is the root cause of the steel crises,"
The back-and-forth reflects rising tensions between the US and China, which President Trump has described as an "economic enemy".
The US has taken two major steps on tariffs recently that have triggered tension with China, the first on steel and aluminium and the second on intellectual property.
The global steel and aluminium tariffs were announced on 8 March. The US is using national security laws to impose the tariffs, which it says are needed to protect US producers.
Certain allies such as Canada, Mexico and the European Union are in line for exemptions, pending talks.
Donald Trump has vowed to cut the US trade deficit with China
China has challenged the US use of national security laws and announced retaliatory tariffs on $3bn (£2.1bn) worth of US products.
Those tariffs went into effect on Monday, targeting US goods including frozen pork, nuts, fresh and dried fruit, ginseng and wine.
The US tariffs related to intellectual property are expected to be set out this week.
They stem from a US investigation into the alleged theft of intellectual property and Beijing's "Made in China 2025" programme, which the US says puts its firms at a disadvantage and unfairly pressures them to share technology, especially in fields such as robotics and telecommunications.
Up to $60bn in tariffs could be imposed on Chinese imports.
China's ambassador to the US, Cui Tiankai, warned Beijing would take counter-measures of "the same proportion".
By Stephen McDonell, BBC News, Hong Kong
China's theft of foreign intellectual property is what sparked all this in the first place, according to Washington. If international companies want to operate in China they must hand over their intellectual property for the privilege, thus delivering the likes of German high-speed rail technology into the hands of Chinese engineers.
Yet now that China's retaliatory tariffs have kicked in, there are also those sympathetic with that argument who are worried that launching a potential tariff war is not the way to fix the problem. Naturally others say China has been getting away with this for years and tough measures were needed in order to force change.
There is also the overall imbalance in US-China trade but a large Chinese surplus, of course, means it is potentially much more exposed during a trade war than America. For this reason Beijing will want to negotiate a way out of this escalating tariff showdown.
Its first set of tariffs are relatively mild but they come in response to the first round of US tariffs and a second has already been announced. There are plenty more American companies to be hit and other nations, especially those in Europe and Asia, could soon find themselves dragged into this conflict.
American businesses caught up in the dispute have raised alarms, noting that China is a large market for certain goods, including pork, soya beans and aircraft.
For example, last year China was the third largest market for US pork, receiving about $1.1bn worth of products, according to the National Pork Producer Council.
"Any restriction on export markets is not a good development for US pork producers," Jim Monroe, a spokesman for the National Pork Producers Council, told the BBC.
US companies have said that while they share some of the Trump administration's concerns, they are worried that threatening tariffs is not the best way to resolve the problems.
"The direction of what the US government is doing, and that is to apply some pressure, use some leverage, to level the playing field is the right one, although I don't think tariffs is the best way to go," said William Zarit. chairman of the American Chamber of Commerce in China.
Mr Zarit told the BBC that members of his organisation, which represents more than 900 companies operating across China, including Intel, Dell, Honeywell and Coca-Cola, were encouraged to hear that top officials have started talking again.
"I think it shows that both sides want to solve this before it gets out of hand," he said.
