WASHINGTON—President Donald Trump’s pledge Thursday to impose stiff tariffs on steel and aluminum imports sparked worries of a looming global trade war, sending stocks tumbling, drawing protests from a broad swath of American industries dependent on the metals, and prompting threats of retaliation across Asia, Europe, and North America.

The move fulfills a Trump campaign promise that helped fuel his surprise 2016 campaign victory in the industrial Midwest, and he told a White House meeting of industry executives that his coming...