U.S. intelligence believes that assailants connected to al Qaeda in Iraq were among the core group that attacked the diplomatic mission in Benghazi, a U.S. government official told CNN.

Previously, intelligence officials said there were signs of connections to al Qaeda in the Islamic Maghreb, the North African wing of the terror group.

The revelation that members of al Qaeda in Iraq are suspected of involvement in the Libya attack comes at a time when there is a growing number of fighters from that group also taking part in the Syrian civil war.

It also surfaces as questions persist about Benghazi security and the Obama administration's response to the attack that have become issues in the presidential campaign. Republicans have said issues around the attack illustrate weaknesses in President Barack Obama's foreign policy.

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The weakened al Qaeda affiliate has had a resurgence in Iraq since U.S. forces left the country at the end of last year. The group had used Libya as a source for fighters. In a 2008 cable, Stevens described a nearby town of Derna as "a wellspring of Libyan foreign fighters" for al Qaeda in Iraq.

The latest intelligence suggests the core group of suspects from the first wave of the attack on the Benghazi mission numbered between 35 to 40. Around a dozen of the attackers are believed to be connected to either al Qaeda in Iraq or al Qaeda in the Islamic Maghreb, the government official said.

The attack had two waves: The first targeted the main compound where Stevens and another diplomatic official were believed killed. A second stage a few hours later involved an annex building approximately a mile away.

According to the official, others in the core group are suspected of having ties to the Libyan group Ansar al-Sharia, and many of them are believed to be Egyptian jihadis.

A suspect in the attack is being held in Tunisia where the United States has been denied access to him, according to Sen. Saxby Chambliss, the ranking Republican on the Intelligence Committee.

Chambliss would not name the suspect, but CNN has been told it is Ali Ani al-Harzi, a Tunisian connected to extremist groups in North Africa.

Details about al-Harzi were first reported by the Daily Beast.

In a statement Chambliss said, "Tunisian authorities have a suspected terrorist in custody, yet our guys aren't able to interrogate him."

An aide to Chambliss said the suspect was first arrested in Turkey and later sent to Tunisia.

CNN has learned that the United States first became aware of al-Harzi when he apparently posted details of the attack on social media while it was happening.

At the request of the United States, Turkish officials detained al-Harzi when he entered that country after leaving Libya. Turkey then transferred him to Tunisia.

The United States fully expects to have access to him and is trying to figure out how that will happen, another U.S. official told CNN. The FBI is leading the investigation and the intelligence community, according to the official, is working behind the scenes to help with that as well.

Video from one security camera at the Benghazi mission was recovered from the site, but a U.S. official would not say whether al-Harzi or any other suspects were identified from the video.

E-mails obtained by CNN made clear that less than 30 minutes after the attack began, the State Department notified officials within the agency, the White House, the Office of the Director of National Intelligence, the Pentagon and the FBI that an attack was underway and that Stevens was in the compound.

And just two hours later, one of the e-mails indicated the Libyan extremist group Ansar al Sharia was claiming responsibility for the attack on social media websites. "Embassy Tripoli reports the group claimed responsibility on Facebook and Twitter and has called for an attack on Embassy Tripoli," the e-mail said.

Rep. Mike Rogers, chairman of the House Intelligence Committee, told CNN the e-mails show the attack was not a spontaneous demonstration in protest of an anti-Muslim video as the intelligence community and Obama administration officials initially claimed.

"So what you saw in the e-mails in that real time was a real description," Rogers told Soledad O'Brien on "Starting Point." "And, as you noticed, there was no talk of demonstrations or other things. And it was clearly very early identified with a terrorist affiliate of AQIM."

Eight hours after the first e-mail was sent by the State Department to officials around the government, another message, obtained by CNN on Wednesday from a government official, said that the personnel in the "shelter location" in Benghazi were "under attack by mortar fire." It added there are reports of injuries to staff.

The timing of the message suggests the "shelter" referenced was the CIA annex a mile from the main diplomatic mission where, ultimately, two former Navy SEALs were killed in an effort to fight the attackers.

The email will likely be cited by critics to show that the administration knew within hours about the military nature of the attack.

Secretary of State Hillary Clinton said the documents did not tell the whole story, describing conclusions drawn from the one document as "cherry picking."

"Posting something on Facebook is not in and of itself evidence, and I think it just underscores how fluid the reporting was at the time and continued for some time to be," Clinton said.

Moreover, intelligence officials do not believe Ansar al-Sharia is solely responsible with indications now that some of the attackers were associated with al Qaeda in Iraq, al Qaeda in the Islamic Maghreb and an Egyptian jihad network.

A spokesman for Ansar al-Sharia denied the group was responsible the day after the assault.