The Turkish military began an offensive in Syria to seize territory held by U.S.-backed Kurdish forces, opening a new front in the war-ravaged country and drawing a renewed defense by President Trump of his decision to shift U.S. troops out of the area, effectively enabling the start of the assault.

Turkish authorities kicked off the operation on Wednesday despite U.S. warnings that it would punish Turkey if it attacked the Kurdish militants, Washington’s partner in the fight against Islamic State in northeastern Syria. The...