A senior Kurdish official, who asked not to be named because he was discussing internal deliberations, said Saturday that the Kurdish authorities had asked the Obama administration several weeks ago to provide ammunition, sniper rifles, machine guns, mortars, vehicles and other equipment for their pesh merga fighters. Though the Iraqi government had recently provided some ammunition, he said, the Americans were still assessing the Kurdish request. “Pesh merga forces were forced to withdraw from engagements with ISIS forces because they ran out of ammunition,” said Michael D. Barbero, a retired Army lieutenant general who helped train Iraqi forces from 2009-11. “We should expedite this support to them.”

Another way to push back against ISIS would be to train and advise the Iraqi forces. The Pentagon sent about 300 Special Operations forces to Iraq to conduct an assessment of its forces, but administration officials have yet to decide whether to mount a substantial advisory effort.

Now that American reconnaissance planes and drones have been tracking ISIS locations, the United States military also has more of the intelligence it would need if the administration elected to broaden the scope of its air attacks.