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The task force includes an active military member, though another senior official involved in the investigation said that neither the military member nor any other person on the task force requested permission to tell the Pentagon’s top leadership about the contacts.

FBI Director Robert S. Mueller III has ordered a full review of the case. An FBI statement issued Tuesday said the review will “determine all of the facts and circumstances related to this tragedy and whether, with the benefit of hindsight, any policies or practices should change based on what we learn.”

A retired FBI agent said the case highlights an underlying problem vexing terrorism investigations.

“The further we get away from 9/11, the less on guard as a nation we become,” said Ken Piernick, who worked as an acting chief in one of the FBI’s counterterrorism sections.

Mr. Piernick said he suspects that investigators have become fatigued after years of chasing down countless tidbits of information and now may look at tips with less scrutiny.

“The problem with that is the concept of ‘hiding in plain sight’ and a bunch of things come into play,” he said.

ABC News first reported Wednesday that Maj. Hasan had “more unexplained connections” to people being tracked by the FBI in addition to Mr. al-Awlaki.

Although the FBI has dismissed the e-mails between Maj. Hasan and Mr. al-Awlaki as “explainable,” the imam has been under investigation by U.S. authorities for several years. He was identified shortly after the Sept. 11, 2001, terrorist attacks on the World Trade Center and the Pentagon as the “spiritual adviser” of two of the terrorist hijackers, Nawaf Alhamzi and Hani Hanjour.

Alhamzi, a Saudi national admitted to the United States on a tourist visa in January 2001, and Hanjour, also a Saudi national admitted to the country in December 2000 on a student visa, had listened to Mr. al-Awlaki preach at the Masjid Al Ribat Al Islami mosque in San Diego and the Dar al-Hijrah Islamic Center in Falls Church.

Maj. Hasan also had attended the San Diego mosque in 2001 to hear Mr. al-Awlaki preach, and later turned up at the Falls Church mosque, although it is unclear whether he met with Alhamzi or Hanjour.

Maj. Hasan who is recovering from gunshot wounds — a civilian police officer shot him to end the rampage — has not been officially charged. The FBI has said he will be charged in a military court.

Investigators say there is no indication Maj. Hasan acted in concert with others or as part of a larger terrorist plot.

But the military intelligence official who spoke to The Times remained skeptical.

“It’s way too early” to be saying Maj. Hasan acted alone, the military intelligence official said, though he acknowledged that Maj. Hasan may just have been inspired by al Qaeda or other Muslim jihad groups without being under their operational control.

“There is definitely a need for a fresh look” at the intelligence breakdown, said the official, who described the case as “an intel debacle.”

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