BMW, Daimler and Volkswagen, which have plants in Mexico to take advantage of lower labour costs and U.S. trade deals with its southern neighbour, were down by as much as 2.9 percent by 0800 GMT.

Shares in Asian auto makers dropped overnight.

Trump said he would hit goods coming from Mexico with a 5% tariff and would hike that levy each month until it hits 25% on Oct. 1, unless Mexico takes immediate action against illegal immigration across the U.S. border.

A spokesman for VW subsidiary Audi said the company was watching developments very closely but it was too early to speculate on outcomes.

A note by car analyst Arndt Ellinghorst described German carmakers as exposed, noting BMW's new plant at San Luis Potosi represented nearly 20% of its production for North America.

An auto industry source said the situation was puzzling in that the migration issues belonged to the political stage and came despite an update to the North American Free Trade Agreement (NAFTA) in the making for this summer.

It also came as the EU and the United States are working to avoid an escalation in trade conflicts.

Commerzbank strategist Ulrich Leuchtmann said: "The U.S. trade policy has taken a qualitatively different turn. Using tariffs as a tool for non-economic goals is something which brings a new quality to proceedings."

(Reporting by Vera Eckert; Additional reporting by Riham Alkousaa in Berlin and Ilona Wissenbach in Frankfurt; Editing by David Holmes)