Malmström added that if the USA removes its tariffs, the European taxes would also be lifted.
The majority of USA goods targeted by the European Union, such as tobacco, Harley Davidson motorcycles, cranberries and peanut butter, will now carry a tariff of 25%.
The imposition of tariffs has raised the specter of a full-blown trade war, which could be costly to consumers, jobs and the global economy. Beijing has vowed to immediately retaliate with its own tariffs on US soybeans and other farm products in a direct shot at Mr. Trump's supporters in America's heartland.
India had sought to be exempt from the new USA tariffs on steel and aluminum, arguing its exports were small in comparison to other countries, but got nowhere.
Late last month, Mr Trump proceeded to infuriate USA allies - from the European Union to Canada and Mexico by imposing tariffs of 25 per cent on imported steel and 10 per cent on aluminium. "Our response will have to be proportionate, reasonable and intelligent".
As painful as the brewing trade war could prove, many have seen it coming.
Colombia 1-2 Japan: Yuya Osako header seals emotional opening win
The Blue Samurai included the experienced duo of midfielder Shinji Kagawa and defender Yuto Nagatomo in their starting line-up. Colombia equalised six minutes before the interval when Juan Quintero's low free kick squeezed over the line.
White House National Trade Council Director Peter Navarro on the Trump administration's proposed Chinese investment restrictions.
Trump has also started a trade fight with China over Beijing's sharp-elbowed efforts to overtake US technological dominance.
Economists note that on the whole, the US and European Union tariffs will not immediately cause great damage to either side's economy.
Trump recently approved heavy tariffs on $50 billion of Chinese imports.
The Chinese have said they will respond in kind. The United States' trade deficit with China a year ago was $376 billion, by comparison.
The Commerce Department is allowing companies to request exemptions from the steel and aluminum tariffs - if they can show that the metals they need aren't available from Americans producers.
Trade representatives from India and the United States are set to meet in New Delhi next week.
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.