Senior counterterrorism officials felt cut out of the loop the night of the attack on the Benghazi consulate, according to emails that were shared with Fox News by military sources who are familiar with discussions of how to respond the night of the Sept. 11 attack.

Top State Department officials decided not to send an interagency rapid response unit designed to respond to terrorist attacks known as a FEST team, a Foreign Emergency Support Team. This team from the State Department and CIA has a military Joint Special Operations Command element to it and has been routinely deployed to assist in investigations -- for instance, after the USS Cole bombing and the bombings at the U.S. Embassies in Kenya and Tanzania.

That team, these counterterrorism officials argue, could have helped the FBI gain access to the site in Benghazi faster. It ultimately took the FBI 24 days.

"The response process was isolated at the most senior level," according to one intelligence source. "Counterterrorism professionals were not consulted and a decision was taken to send the FBI on its own without the enablers that would have allowed its agents to gain access to the site in Benghazi in a timely manner." The FBI team did not get on the ground in Benghazi for several weeks after the attack and at that point any "evidence" had been rifled through by looters and journalists.

"A better response approach could have certainly allowed the FBI to access the site much sooner than the 24 days it would eventually take," a source in the counterterrorism community said.

More On This...

Further, the Counterterrorism Security Group, or CSG, was never asked to meet that night or in subsequent days, according to two separate counterterrorism officials, as first reported by CBS News. The CSG is composed of experts on terrorism from across government agencies and makes recommendations to the deputies who assist the president's Cabinet in formulating a response to crises involving terrorism.

National Security Council spokesman Tommy Vietor told Fox News, "the most senior people in government worked on this issue from the minute it happened. That includes the Secretary of Defense, Chairman of the Joint Chiefs, Secretary of State, National Security advisor, etcetera. Additionally, the Deputies Committee -- the second in command at the relevant national security agencies -- met at least once and more often twice a day to manage the issue."

But the latest revelations, including reporting by Fox News that the State Department was warned a month before the attack that the consulate could not withstand a coordinated strike, have sparked renewed criticisms from top GOP lawmakers.

"Enough already, Mr. President," Lindsey Graham, R-S.C. said in a statement. "You need to address the American people and account for your leadership in the attack on our Consulate in Benghazi, Libya. You should explain to the American people what you knew, when you knew it, and what you did about it before, during and after the attack."

Several government spokesmen suggest that the president's top advisers were meeting that night to oversee the response, suggesting the employment of the Counterterrorism Security Group was not necessary.

As to why the FEST was not sent, State Department spokesman Philippe Reines responded that "the first thing to know is that it's not a security team. It's primarily a resource that State can send to help restore a facility. Best example is Nairobi after the bombing because the Embassy suffered such significant damage. It couldn't function properly without resuming basic infrastructure needs like communications. In this case, that was not necessary as Embassy Tripoli wasn't impacted and could, as it does today, continue to function normally."

Administration officials didn't know in the initial hours whether they had a potential hostage situation. According to an account now provided by the CIA and quoted by the Washington Post's David Ignatius, at 1:15 a.m. (more than three hours after the attack began) when Stevens was still missing: "the first idea is to go to a Benghazi hospital to recover Stevens, who they rightly suspect is already dead. But the hospital is surrounded by the al-Qaeda-linked Ansar al-Sharia militia that mounted the consulate attack."

This part of the CIA timeline released by the agency on Thursday suggests that the night of the attack, the CIA's Global Response Staff, or GRS, agents knew that an Al Qaeda-linked group was at the hospital where the ambassador's body had been taken -- and yet days later the CIA provided talking points to the administration before U.S. Ambassador to the U.N. Susan Rice went on five separate Sunday talk shows and made no mention of terrorism.

Fox News has learned that U.S. military intelligence was informing senior commanders as early as 7 p.m. ET -- less than four hours after the attack began -- that Ansar al-Sharia carried out the attack. The intelligence was relayed to the military with no caveats, according to a source familiar with the intelligence.

Further, Fox News has been shown two independent State Department cables, which have now been published by Foreign Policy magazine, that show that on the day of the attack Stevens' team sent cables expressing concern that the consulate was under surveillance. At least one of the cables says the Libyan police themselves -- the security force provided to the U.S. consulate by the Minister of Foreign Affairs -- was photographing the Consulate at 6:43 a.m. on the morning of the attack.

U.S. intelligence officials tell Fox News there were reports from eyewitnesses in Benghazi on Sept. 11 that an armed militia was gathering three hours before the attack on the consulate began at 9:47 p.m.