Story highlights Secretary of State Hillary Clinton says don't "cherry pick" documents

The White House says it received conflicting information about the attack

A government email on the day of the attack says an Islamist group claimed credit

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

Two hours after first being notified of an attack on the U.S. diplomatic mission in Benghazi, Libya, a government e-mail to the White House, the State Department and the FBI said an Islamist group had claimed credit, according to a copy obtained by CNN.

An initial e-mail was sent while the attack was still underway, and another that arrived two hours later -- sent from a State Department address to various government agencies including the executive office of the president -- identified Ansar al-Sharia as claiming responsibility for the attack on its Facebook page and on Twitter.

The group denied responsibility the next day.

However, the e-mails raise further questions about the seeming confusion on the part of the Obama administration to determine the nature of the September 11 attack that left U.S. Ambassador Christopher Stevens and three other Americans dead.

Two White House officials, speaking on condition of not being identified on Wednesday, said the government e-mails about the attack were not an intelligence assessment. They also noted that there was conflicting information about Ansar al-Sharia denying responsibility.

"They were a part of the many different reports we were receiving that day," one of the White House officials said of the e-mails. "There are always multiple and conflicting reports in the initial hours of an attack. That's why you have an investigation."

Photos: Photos: Attack on U.S. mission in Benghazi Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Attackers set the U.S. mission in Benghazi, Libya, on fire on September 11, 2012. The U.S. ambassador to Libya, Christopher Stevens, and three other U.S. nationals were killed during the attack. The Obama administration initially thought the attack was carried out by an angry mob responding to a video, made in the United States, that mocked Islam and the Prophet Mohammed. But the storming of the mission was later determined to have been a terrorist attack. Hide Caption 1 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Obama and Clinton stand at Andrews Air Force Base as the bodies of the four Americans killed are returned on September 14. Hide Caption 2 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A desk sits inside the burnt U.S. mission on September 13, two days after the attack. Hide Caption 3 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Damage is seen inside the U.S. mission on September 13. Hide Caption 4 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A lounge chair and umbrella float in the swimming pool of the U.S. mission on September 13. Hide Caption 5 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Demonstrators gather in Libya on September 12 to condemn the killers and voice support for the victims. Hide Caption 6 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – U.S. President Barack Obama, with Secretary of State Hillary Clinton on September 12, makes a statement at the White House about Stevens' death. Hide Caption 7 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A burnt vehicle is seen at the U.S. mission in Benghazi on September 12. Hide Caption 8 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – People inspect the damage on September 12. Hide Caption 9 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A small American flag is seen in the rubble on September 12. Hide Caption 10 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A man stands in part of a burned-out building of the U.S. mission on September 12. Hide Caption 11 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Smoke and fire damage is evident inside a building on September 12. Hide Caption 12 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Half-burnt debris and ash cover the floor of one of the U.S. mission buildings on September 12. Hide Caption 13 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – The U.S. mission is seen in flames on September 11, the day of the attack. Hide Caption 14 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A protester reacts as the U.S. mission burns on September 11. Hide Caption 15 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A vehicle and the surrounding area are engulfed in flames on September 11. Hide Caption 16 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Flames erupt outside of a building on September 11. Hide Caption 17 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A vehicle burns during the attack on the U.S. mission on September 11. Hide Caption 18 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Onlookers record the damage from the attack on September 11. Hide Caption 19 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – Onlookers walk past a burning truck and building on September 11. Hide Caption 20 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – A vehicle sits smoldering in flames on September 11. Hide Caption 21 of 22 Photos: Photos: Attack on U.S. mission in Benghazi Attack on U.S. mission in Benghazi – People duck flames outside a building on September 11. Hide Caption 22 of 22

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Secretary of State Hillary Clinton advised reporters to wait until a review panel she appointed to investigate what happened completed its work.

"The Independent Accountability Review Board is already hard at work looking at everything, not cherry picking one story here or one document there but looking at everything, which I highly recommend as the appropriate approach to something as complex an attack like this," Clinton said Wednesday.

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

She repeated her earlier pledge to "take whatever measures are necessary to fix anything that needs to be fixed, and we will bring those to justice who committed these murders."

Meanwhile, White House spokesman Jay Carney noted the e-mail about the claim of responsiblity "was an open-source, unclassified e-mail referring to an assertion made on a social media site that everyone in this room had access to and knew about instantaneously."

Carney added that "the whole point of an intelligence community and what they do is to assess strands of information and make judgments about what happened and who was responsible."

The day after the attack took place, President Barack Obama referred to it as an "act of terror."

But in the following days, 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.

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 -- two days after the attack -- 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.

However, it wasn't until September 19 that Matthew Olsen, the nation's counterterrorism chief, told senators that it was a terrorist attack. The next day, Carney also said it was "self-evident that what happened in Benghazi was a terrorist attack."

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

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

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

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

The final e-mail, at 6:07 p.m., noted the claim of responsibility for the attack. The subject line said: "Update 2: Ansar al-Sharia Claims Responsibility for Benghazi Attack."

"Embassy Tripoli reports the group claimed responsibility on Facebook and Twitter and has called for an attack on Embassy Tripoli," the e-mail said.

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."

It is common for one or more claims of responsibility to follow high-profile attacks on U.S. targets, and intelligence officials analyze them for validity before declaring any legitimate. For example, groups make false claims to seek publicity and raise their profile.

Analysts examine a group's history, whether it made previous claims that were legitimate, whether it has the capacity to carry out such an attack, and whether known members of the group participated in the attack in assessing the validity of claims of responsibility.