TAMPA, Fla.—The U.S. and Iraq have begun preparations for an assault by summer to retake Mosul, selecting and training military units and cutting supply lines to Islamic State militants who control Iraq’s second-largest city, the top American commander in the Middle East said.

Gen. Lloyd Austin, the head of the military’s Central Command, told The Wall Street Journal that the international campaign against Islamic State has inflicted significant damage. Opposing forces have reclaimed about 300 square miles of territory in Iraq and killed some 6,000 members of the Sunni radical group, eliminating about half its leadership.

U.S. defense officials have bristled under criticism from Iraqi officials and others that the campaign against Islamic State is stalled or moving too slowly. U.S. Central Command is eager to show that airstrikes are having an effect on the ground and that the American and Iraqi militaries have a plan to continue to drive fighters out of their key strongholds in Iraq.

U.S. officials said they don’t have a good estimate of the current size of Islamic State forces, although they were once estimated at up to 14,000. They concede that Islamic State fighters still control large parts of northern and western Iraq, but say much of the Kurdish-controlled areas have been reclaimed. Islamic State captured Mosul, a city of 600,000, in June at the start of its blitz across parts of Iraq.

On Wednesday and Thursday, U.S. airstrikes focused on cutting supply lines between militants who control Mosul and Islamic State’s stronghold in Syria. The planes conducted 18 strikes near Mosul and Sinjar, hitting Islamic State fighters, staging positions and armored vehicles, according to the U.S. military.