The trade dispute between the world's two largest economies escalated after Trump said in a statement late Monday that he had requested the United States Trade Representative to identify $200 billion worth of Chinese goods for additional tariffs at a rate of 10 percent.
Last week Mr Trump announced the United States would impose 25% tariffs on $50bn worth of Chinese goods.
China's commerce ministry said Beijing will fight back firmly with "qualitative" and "quantitative" measures if the United States publishes an additional list of tariffs on Chinese goods, accusing Washington of launching a trade war.
The president asserted in a statement Monday night that China is determined "to keep the United States at a permanent and unfair disadvantage".
That happened after the US President gave some clues about the possibility for introducing new tariffs on the US $200 billion worth of Chinese goods.
The Trump administration also has threatened a tariff hike on another $100 billion of imports in its parallel dispute over Beijing's trade surplus, though it has yet to say when that might take effect.
Trade frictions between the United States and Canada have been particularly strained in recent weeks, with Trump taking umbrage at remarks by Canadian Prime Minister Justin Trudeau that were critical of the heavy US tariffs.
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Stocks are trading lower at midday Tuesday on fresh worries about a trade dispute between the US and China, although they've recovered somewhat from an early slump. "The problem is, such a tactic is unlikely to work with China", said Kota Hirayama, senior emerging markets economist at SMBC Nikko Securities Inc in Tokyo.
The Dow Jones industrials are down 291 points, or 1.2 percent, to 24,697, after dropping more than 400 points in morning trading. That might cut into demand for the device, acting as an extra tax on USA consumers, but it would protect Apple's profit margins on its popular smartphone line. -China trade spat and as base metal prices slid.
The global sell-off came after President Donald Trump threatened to put tariffs on another $400 billion in imports from China, and the Chinese government said it would retaliate. China has already said it will retaliate for last week's move and said it would escalate its response if further tariffs were imposed.
Commodities also sold off on trade concerns.
According to the New York Times article, Trump promised Cook that he wouldn't place tariffs on iPhone assembled in China.
"President Trump will have the backs of all Americans who may be targeted by Chinese actions and with respect to the farmers in Iowa or any other state", Navarro said.
Bruce Blakeman, vice-president for the Asia Pacific region of Cargill Inc, the USA agricultural conglomerate, said the corporation is deeply concerned by Washington's actions in issuing tariffs on Chinese products based on Section 301 of the Trade Act of 1974.