The White House has criticised China after it imposed retaliatory tariffs against the US on a range of goods, including pork and wine.
Beijing has introduced duties of up to 25% on 128 American imports following President Donald Trump's decision to slap tariffs on 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 Asian shares traded lower as trade war fears mount.
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 was off 1% and the Hang Seng down by 0.6% in afternoon trading.