The focus on the Khorasan Group in recent days has, at least for the moment, diverted attention from the Islamic State, the militant group whose recent battlefield successes were Mr. Obama’s original reason for launching airstrikes. It has also underscored the enduring relevance of Al Qaeda’s leadership apparatus in Pakistan, a group that Mr. Obama told the United Nations on Wednesday had been badly battered.

“There’s a contradiction here,” said Bruce O. Riedel, a former C.I.A. analyst now at the Brookings Institution. “If they are that decimated, why are we so alarmed when we detect new evidence of their activities?”

The paucity of public information about the Khorasan Group makes it hard to draw firm conclusions about its ultimate goals. Intelligence officials and terrorism experts believe that the group, although based in Syria, answers ultimately to Mr. Zawahri and Al Qaeda’s core leadership in Pakistan. They said that its size seemed to fluctuate, but that it consisted of approximately two dozen operatives, most of whom came to Syria from Pakistan and Afghanistan beginning in 2012.