“The president has taken no option off the table, and there are current discussions taking place,” Mr. Kerry said when asked if the White House had settled for containment and forsworn a more ambitious effort to roll back ISIS’ gains that could commence when a new Iraqi government forms.

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.

Iraqi officials first floated the idea of airstrikes a year ago, and Prime Minister Nuri Kamal al-Maliki asked the United States to consider airstrikes in a May conversation with Vice President Joseph R. Biden Jr. The White House began to make clear that airstrikes were an option after the fall of Mosul in June.

The threat that the United States is confronting in ISIS is not an entirely new one, and the danger the militants present to the Yazidi minority, which appeared to catch the administration by surprise and prompted Mr. Obama to authorize airstrikes, was foreshadowed seven years ago.