Hundreds of contractors working for America’s biggest defense companies are taking on a broader role in helping Iraq’s military learn to use new weapons in a growing battle against Islamist insurgents.

Over the next few months, the U.S. government is expected to begin sending more than $6 billion in military equipment to Iraq. The latest deal includes 24 Apache attack helicopters made by Boeing Co. BA -0.84% and nearly 500 Hellfire missiles produced by Lockheed Martin Corp.

While the helicopters may not arrive in time to help with the current fighting, the missiles are expected to be used by the Iraqi military in the battle to uproot Islamic fighters from Ramadi and Fallujah, cities that were the focus of major U.S. military operations during the height of the war in Iraq. […]