The EU's reactive charges on €2.8bn (£2.4bn) worth of USA goods came into force on Friday morning, with European Commission president Jean-Claude Juncker slamming the White House for acting against "all logic and history".
In two weeks, the U.S. is due to start taxing $US34 billion in Chinese goods.
The world's most-powerful central bankers this week warned that escalating worldwide trade tensions have started damaging confidence among companies, threatening the global economic expansion.
Even before Mr Trump's latest threat, some United States companies in China were feeling the pressure.
EU Trade Commissioner Cecilia Malmstrom said this week that the 28-nation bloc was "left with no other choice" but to impose tariffs of its own after the "unilateral and unjustified decision of the U.S.". "The U.S.is abusing the tariff methods and starting trade wars all around the world".
Trump threatened additional taxes on European cars if the EU chose to retaliate.
The spat comes amid a wider push by President Trump's administration to hit other countries with tariffs that would reduce the US trade deficit. "The EU perhaps will find a few disgruntled consumers who have to pay more for their Harley Davidsons, but that is not a big loss for us".
"We've never seen anything like this", said Mary Lovely, a Syracuse University economist who studies global trade - at least not since countries tried to wall themselves off from foreign competition during the Great Depression.
Trump last week carried out a threat he made earlier this year by announcing he would impose $50 billion worth of tariffs on Chinese goods.
For Americans, new auto tariffs would likely mean higher car prices for both imported and domestically manufactured vehicles.
"If you have trade barriers and restrictions, we can not create as many jobs as we are planning to", Volvo Cars CEO Hakan Samuelsson told Reuters at an event celebrating the new facility. The potential trade action would affect more than $200 billion in USA imports, PIIE said.
"No, because the United States is both an important export market and a strong production base for us", Mattes said. All told, the $450 billion in potential tariffs would cover almost 90 percent of goods China sends to the United States.
Sen. Orrin Hatch, who opposes the auto tariffs, did the math for Commerce Secretary Wilbur Ross at a hearing this month.
"We've never seen anything like this", said Mary Lovely, a Syracuse University economist who studies worldwide trade - at least not since countries tried to wall themselves off from foreign competition during the Great Depression.