WASHINGTON — The American air campaign to thwart the advance of fighters from the Islamic State has been the easy part of President Obama’s strategy in Iraq and Syria. Soon begins the next and much harder phase: rolling back their gains in Mosul, Falluja and other populated areas, which will require American advisers to train and coordinate airstrikes with Iraqi forces.

Pentagon officials are more willing than their counterparts at the White House to acknowledge that this will almost certainly require American Special Operations forces on the ground to call in airstrikes and provide tactical advice to Iraqi troops. “There is no one in this building who does not know that clearing out the cities will be much harder,” a senior Defense Department official said in an interview. “That’s when the rubber is going to meet the road.”

Gen. Martin E. Dempsey, the chairman of the Joint Chiefs of Staff, this week described this phase as “extraordinarily complex.”

Urban warfare in Iraq has been challenging for the United States, which had 70 troops killed in the second battle of Falluja in 2004 and fought hard to regain control of cities like Mosul, Baquba and Baghdad. So it will be even harder for the Iraqis, who have so far proved ineffective in combating the Islamic State, also known as ISIS or ISIL.