“It is a balance between letting them develop their own plan and take ownership for it, and ensuring that they don’t stretch themselves too far and outpace their capability,” said one United States military official, who asked not to be identified because he was discussing war planning.

Though the United States began to carry out airstrikes to protect Erbil in August, the longer-term campaign plan has remained under wraps. Now that the planning has advanced, more than a dozen Iraqi and American officials provided details about a strategy that is certain to become increasingly visible.

The basic strategy calls for attacking fighters from the Islamic State, also known as ISIS or ISIL, with a goal of isolating them in major strongholds like Mosul.

That could enable Iraqi troops, Kurdish pesh merga units and fighters that have been recruited from Sunni tribes to take on a weakened foe that has been cut off from its supply lines and reinforcements in Syria, which are subject to American airstrikes.