President Obama may or may not be right when he claims, as he often does, that “the core of Al Qaeda in Afghanistan is on the way to defeat.” But it is clear that the broader movement of violent Islamism, which has been identified with al-Qaeda but which is actually much broader, is far from defeated.

Consider just the terrible news of the past weekend.

In Nairobi, a squad of gunmen from the Somali group al-Shabab have massacred at least 68 people in an upscale mall while holding others hostage–an attack reminiscent, albeit on a slightly smaller scale, of the Mumbai terrorist attack of 2008.

In Iraq, one suicide bomber blew himself up at a funeral in Baghdad, killing at least 16 and wounding more than 30, while another blew up in a residential area of Kirkuk, wounding at least 35 people. These are the latest in a series of terrible attacks in Iraq, which, according to the Associated Press, have seen “more than 4,000 people … killed between April and August, a level of carnage not seen since 2006 to 2008, when Iraq was nearing civil war.”

Yet another suicide attack in Peshawar, Pakistan, killed at least 78 people, including 34 women and seven children, at a church. This was presumably the handiwork of the Pakistani Taliban.

Oh, and two Israeli soldiers were slain in the West Bank, one by a sniper, the other by a duplicitous Palestinian acquaintance.

All of these attacks do not suggest that Islamist groups are on their way to seizing power in countries from Somalia to Pakistan. Indeed, the Shabab attack was, in many ways, a sign of the group’s weakness in Somalia, where it has suffered defeats on the ground from Kenyan and African Union troops. Shabab is turning to terrorist attacks against soft targets in Uganda and Kenya to remain relevant.

But what these attacks show is that Islamist groups–some of them affiliated with al-Qaeda, others not–are far from defeated. They still have considerable capacity to wreak carnage and, given the weakness of regimes that are fighting them across the Middle East and Africa, they can make substantial inroads into failed states.

President Obama and the American national security establishment have been too focused on “core” al-Qaeda while downplaying the menace from these other groups on the periphery, which continue to pose as big a threat as ever.