WASHINGTON — Two hours after the attack on the U.S. consulate in Benghazi, the White House, the State Department and the FBI were told that an Islamist group had claimed credit, government e-mails obtained by CNN show.

One of the e-mails — sent from a State Department address to various government agencies — specifically identifies Ansar al-Sharia as claiming responsibility for the attack on its Facebook page and on Twitter.

The e-mails raise further questions about the seeming confusion on the part of the Obama administration to determine the nature of the September attack and those who planned it.

The attack left U.S. Ambassador Christopher Stevens and three other Americans dead.

The day after it took place, President Barack Obama labeled the incident an “act of terror.”

But in the days following the attack, White House spokesman Jay Carney maintained there was no evidence suggesting the attack was “planned or imminent.”

The administration also suggested that an anti-Muslim video produced in the United States likely fueled a spontaneous demonstration in Benghazi as it had in Cairo, where the U.S. Embassy also was attacked.

U.S. Secretary of State Hillary Clinton, State Department spokeswoman Victoria Nuland and Susan Rice, U.S. ambassador to the United Nations, all cited the video as a motivating factor in the attack.

On September 13, a senior U.S. official told CNN that the violence in Libya was not the work of “an innocent mob.”

“The video or 9/11 made a handy excuse and could be fortuitous from their perspective, but this was a clearly planned military-type attack,” the official said.

But it wasn’t until September 19 that the administration began to call the attack the work of terrorists.

The e-mails provide additional insight into the Benghazi attack.

The first one, sent at 4:05 p.m. ET, or 10:05 p.m. in Libya, describes a diplomatic mission under attack.

“Approximately 20 armed people fired shots; explosions have been heard as well,” the e-mail says. Stevens and four other mission staff are in the compound safe haven, it added.

Less than an hour later at 4:54 p.m. ET, another e-mail reports “firing at the U.S. Diplomatic Mission in Benghazi has stopped and the compound has been cleared.” It says a search was underway for consulate personnel.

The final e-mail, from 6:07 p.m., notes the claim of responsibility for the attack.

The subject line reads: “Update 2: Ansar al-Sharia Claims Responsibility for Benghazi Attack.”

The email says: “Embassy Tripoli reports the group claimed responsibility on Facebook and Twitter and has called for an attack on Embassy Tripoli.

The Facebook claim of involvement was subsequently denied by the group at a news conference in the following days, but not very convincingly.

“We are saluting our people for this zeal in protecting their religion, to grant victory to the prophet,” a spokesman for Ansar al-Sharia said at the time. “The response has to be firm.”

— CNN’s Ed Payne, Tim Lister and Adam Levine contributed to this report