The Commerce Department said Wednesday it has exempted some steel products from Japan and four other countries from USA tariffs of 25 percent.
Together with USA tariffs against Mexico and Canada, the trade battles have raised the specter of a global trade war, spooking financial markets that fear major consequences to the global economy.
Trump posted his threat on Twitter the day European Union reprisals took effect against US tariffs on European steel and aluminum. In two weeks, the United States will start taxing $34 billion worth of Chinese goods.
But Mr Katainen said in the same interview the European Union was desperate to avoid a public trade spat.
"Clarity [is] still lacking about how far things will ultimately go between [the] US and China and the potential ripple effect for world trade", said financial analyst Mike van Dulken. A group representing major USA and foreign automakers has said it was "confident that vehicle imports do not pose a national security risk". Leaders from the UK, Germany, and France slammed Trump's decision to hit the European Union with steel and aluminum tariffs, and the bloc responded with tariffs of its own.
Canadian Prime Minister Justin Trudeau this week said the integration of the auto industry in the US and Canada means he has "a hard time accepting that any leader might do the kind of damage to his own auto industry that would happen if he were to bring in such a tariff on Canadian auto manufacturers", Reuters reported.
The EU trade commissioner acknowledged that it had targeted some iconic American items to increase political pressure on the US President and senior US politicians.
U.S. Commerce Secretary Wilbur Ross said earlier this week that his department plans to wrap up by July or August an investigation into whether imported cars and auto parts are a threat to national security.
The Alliance of Automobile Manufacturers, representing major USA and European automakers, said "tariffs raise vehicle prices. limit consumer choice and invite retaliatory action by our trading partners. How they'll take it, we'll have to wait and see".
During his presidential campaign, Trump promised to apply tariffs, saying countries around the world had been exploiting the U.S.
American tariffs on steel and aluminum have also hit Canada, Mexico, India, Turkey and China.
There could be yet another round of USA tariffs.
"Exclusions generally are granted if there is no domestic availability and there are no overriding national security concerns", the department said in a statement.
The United States now imposes a 2.5% tariff on imported passenger cars from the European Union and a 25%tariff on imported pickup trucks.
The rising tensions and the chaos surrounding the steel and aluminum tariffs are starting to generate pushback on Capitol Hill.
The United States' trade deficit with China a year ago was $376 billion, by comparison. Senators this week grilled Commerce Secretary Wilbur Ross.
Shares in major European vehicle companies were already on edge due to trade tensions.