The European Commission said it would start charging import duties of 25 per cent on products including bourbon, jeans and motorbikes, in response to the USA decision to impose tariffs on EU steel and aluminium at the start of the month.
In trade wars, there tend to many casualties and few winners.
A drop in Japan's Topix index brought the week's decline to nearly 3 percent, while equities also fell in China and Hong Kong.
Economists note that on the whole, the USA and European Union tariffs will not immediately cause great damage to either side's economy.
Brussels imposed the raft of duties on USA products worth 2.8 billion euros (£2.45 billion) in a tit-for-tat response to Mr Trump's decision to slap stiff tariffs on European steel and aluminium exports. "Needless to say, if the US removes its tariffs, our measures will also be removed".
"He is using his "irrationality" as a tactic and he is trying to confuse us", said Chen Fengying, an economics expert at state-backed China Institutes of Contemporary International Relations.
The EU exported some 5.5 million tons of steel to the US past year.
The U.S. Trade Representative said in April that the United States' trade deficit with India had fallen to $23 billion in 2017, a 6 percent decrease, as U.S. goods exported to India rose almost $26 billion, up 18 percent from the previous year.
Mr Trump said the global oversupply of those metals - driven by China - threated American steel and aluminium producers.
"China is in full combat mode and prepared to strongly respond to any probable threat or economic assault from Trump", the Global Times reiterated in its report.
Even before Mr Trump's latest threat, some U.S. companies in China were feeling the pressure.
One thing that may cause Beijing to hold back from a full-scale attack on American companies is concern about the impact it would have on the domestic economy.