WASHINGTON—At a closed-door gathering of Gulf states in Jeddah, Saudi Arabia, in May, Defense Secretary Chuck Hagel and his Arab counterparts all signaled agreement on one thing for the first time: Islamist forces seizing territory in Syria and Iraq had become a regionwide menace that can't be ignored.

What they didn't agree on was what to do about it, U.S. officials said.The fall this week of the Iraqi cities Mosul and Tikrit to the Islamic State of Iraq and al-Sham rebel group shows how the insurgent threat is outpacing...