The “what next question” is a worry for an increasing number of U.S. diplomats and intelligence officers. Successive Israeli attacks on Gaza over the last years have splintered Gaza’s militant groups — strengthening some, such as certain elements in the Popular Resistance Committees and Islamic Jihad, that are far more radical than Hamas. In 2007, again in 2009, and then just last May, the Hizb ut-Tahrir movement, which calls for the establishment of a caliphate to “liberate the Holy Land,” held rallies in Hebron and Ramallah that attracted a small but dedicated band of followers.

“In the American media, it’s ‘Hamas, Hamas, Hamas,'” Yousef Munayyer, the executive director of the Jerusalem Fund, said. “It’s a great talking point, but this shouldn’t be about talking points. Israel’s actions are radicalizing Palestinian society. Maybe that’s what they want, but I can’t imagine that’s what we want.”

While Israeli officials might lump Hamas in with ISIS, the group itself has been increasingly worried about the emergence of more radical Islamist movements. This could be clearly seen in the immediate aftermath of the June 12 kidnapping and murder of the three Israeli teens, which took Hamas’s leadership by surprise. “They were caught flat-footed,” the senior Fatah official with whom I spoke confirmed. “They didn’t order the kidnapping or the murder and were surprised it happened. We ourselves thought it wasn’t aimed at Israel, but at breaking up the unity agreement.”