ABOARD THE USS ABRAHAM LINCOLN IN THE NORTH ARABIAN SEA—The commander of U.S. forces in the Middle East said he may recommend a return to a larger U.S. military presence in the area after concluding that the deployment of this aircraft carrier and other capabilities helped curtail Iranian threats.

Gen. Frank McKenzie, head of U.S. Central Command, asked in early May that the carrier, bombers, troops and an antimissile system be sent to the region after learning of “specific” threats against U.S. and allied forces and interests...