Speaking at the World Economic Forum in Davos, Switzerland, Trump warned of the tariffs if the EU did not agree to a trade deal. The EU and the United States have recently locked horns over issues ranging from a French digital tax to aircraft subsidies.
The threat prompted a response from Germany's ambassador to the United States, Emily Haber, that the EU could also impose duties on U.S. products.
The pan-European STOXX 600 index was 0.1% down, having touched a record high of 424.94 earlier in the day.
Automobile stocks were the worst performing sector, dropping more than 1% to their lowest since mid-October. The tariffs threaten to increase pressure on a sector that has already been grappling with a fall in global demand.
Finnish tyre maker Nokian Tyres and German car maker Daimler were the top losers on the auto subindex.
Losses in the STOXX 600 were somewhat tempered by anticipation of a European Central Bank meeting on Thursday, while news of Chinese measures to contain a new virus also lent some support.
While the ECB is widely expected to stand pat on its benchmark interest rate during its first meeting in 2020, investors will be watching for the bank's outlook for the year, with economic growth in the bloc seen bottoming out.
"What you normally see before a big event, which is the ECB tomorrow, is that markets are basically not moving too much," said Teeuwe Mevissen, senior market economist at Rabobank in Amsterdam.
Italy's FTMIB lagged after reports that Luigi di Maio would step down as the leader of the co-ruling 5-Star Movement, stirring fresh election uncertainty.
Frankfurt's DAX fell 0.3%, having touched a record high earlier in the day following a survey on Tuesday that showed a U.S.-China trade truce had lifted German investor morale to its highest since 2015.
German agrigoods maker K&S AG was the worst performer on the STOXX 600 after Bank of America resumed coverage of the stock with an "underperform" rating.
On the other hand, Norway's Gjensidige was the best performer on the STOXX 600, ending at a record high after the insurer posted better-than-expected fourth-quarter earnings and set an extra dividend on top of its normal payout to shareholders.
By Ambar Warrick