JACKSON HOLE, Wyo.—Federal Reserve Chairman Jerome Powell gave his most forceful warning yet about the risks to the U.S. economy from escalating trade tensions and the limits to the central bank’s ability to cushion any fallout.

Mr. Powell, in a widely anticipated speech here Friday, signaled the central bank would follow its rate cut last month, its first in more than a decade, with an additional reduction soon. But he stopped short of saying how much stimulus the Fed might provide beyond that.

Instead,...