The EU's top trade official on Tuesday said the decision of Harley-Davidson to shift some manufacturing of its iconic motorcycles overseas, which President Donald Trump criticised, was a natural consequence of a protectionist US trade policy.

"We don't want to punish, but that is the unfortunate consequence, that (US companies) will put pressure on the American administration to say hey, hold on a minute, this is not good for the American economy," EU Trade Commissioner Cecilia Malmstrom told a news briefing.

Malmstrom spoke just hours after the announcement by the company founded in the early 1900s, which is also suffering under higher steel costs following tariffs enacted by US President Donald Trump.

The European counter-measures to Trump's 25 percent tariff on steel and 10 percent on aluminium did not specifically target companies, but some sectors were chosen by Brussels for their symbolism.

In the early days of his administration Trump had embraced Harley-Davidson, which sells about 40,000 motorcycles a year in Europe, as an emblematic US industrial firm.

"Surprised that Harley-Davidson, of all companies, would be the first to wave the White Flag," the president tweeted on Monday.

Trump has also threatened fresh tariffs on European auto imports, which would especially punish Germany, home of Volkswagen, BMW and Daimler.