A challenge for investigators is sorting out a potential thicket of psychological, ideological or religious motivations behind Hasan’s alleged actions. Hasan’s possible contact with extremists such as Aulaqi would complicate matters, suggesting that U.S. authorities may have missed chances to prevent the cleric from instigating this incident and others. But if it turns out that Hasan acted in the throes of an emotional breakdown, his questionable ties could be misinterpreted in ways that damage U.S. outreach to the Muslim world or provoke an overreaction that divides Americans.

“There’s a massive effort here to look at the Web sites he visited,” the law enforcement official said, speaking on the condition of anonymity because of the ongoing probe. “That’s part of what’s ongoing: what you learn from it, then you’ve got to figure out what it means.” He added: “The important thing is, the jury’s still out on motivation.”

A former senior U.S. counterterrorism official said that “connections to Aulaqi would be problematic on many levels,” calling him “a radicalizer of the first order” with many al-Qaeda ties.

“That said, many people attended that mosque who are not terrorist suspects,” the official said.