The back-channel discussions over the bases, which have not previously been reported, highlight the White House’s uncertainty about escalating its low-level air war against the Islamic State. President Barack Obama proudly pulled all U.S. troops out of Iraq in late 2011. He has repeatedly stressed that the military campaign there that began Aug. 8 will be limited in both scope and duration. With broad swaths of Syria and Iraq under Islamic State control, key U.S. allies are pressing the administration to step up the fight. Taking off from Iraqi bases would make it much easier to do so because it would put the American aircraft closer to their targets.

“Everything is harder when you’re doing it from the outside,” a senior military official said.

At issue is a little-noticed aspect of this air campaign: None of the strikes against Islamic State targets inside Iraq have been carried out by U.S. aircraft based inside Iraq. Since the bombs began falling, U.S. aircraft have carried out more than 84 strikes. F-18s taking off from the aircraft carrier George H.W. Bush, which is in the North Arabian Sea, conducted more than a third of those strikes. The remainder were carried out by U.S. aircraft assigned to bases inside Qatar and other nearby countries.