WASHINGTON—The Pentagon is removing some U.S. missile systems from the Middle East in October, U.S. military officials said, a move that will leave American allies with fewer defenses as the White House ramps up its rhetoric against what it says are threats posed by Iran.

Defense Secretary Jim Mattis is pulling four Patriot missile systems out of Jordan, Kuwait and Bahrain next month in a realignment of forces and capabilities as the military steps up its focus on threats from China and Russia, multiple senior military officials...