U.S. officials are investigating whether the murder Tuesday of the U.S. ambassador to Libya Christopher Stevens and three other American officials was a "coordinated" strike timed for the 11th anniversary of the Sept. 11 attacks -- and not the result of a protest against an anti-Islam film.

A senior administration official told Fox News they are exhaustively investigating every angle of the attack in Benghazi, and an earlier assault on the U.S. Embassy in Cairo, Egypt, and there are early signs the Benghazi assault may have been planned. The official cautioned, though, that the administration has not jumped to any conclusions about what happened, saying it would be "premature" to do so.

But current and former U.S. lawmakers, and others, claimed Wednesday that the attack looked like a coordinated strike.

"Absolutely, I have no doubt about it. It was a coordinated, military-style, commando-type raid," House Intelligence Committee Chairman Mike Rogers told Fox News. Based on his own briefings, Rogers said "military movements" were involved.

"This was a well- planned, well-targeted event. No doubt about it," Rogers said. He said the Al Qaeda-linked Imprisoned Omar Abdul Rahman Brigades is one group being looked at by officials.

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Senior administration officials, meanwhile, described the harrowing details of the firefight Tuesday night in which four people were killed -- though the cause of death for them is unclear -- and three wounded. One official said the compound began taking fire at 10 p.m. local time, touching off an hours-long scramble to retake the building. Shortly afterward, those with Stevens lost track of him -- it wasn't until dawn that his body was returned to U.S. personnel.

Benghazi staff have since been evacuated, while the staffing in Tripoli has been reduced to emergency levels. Officials could not say whether a protest had anything to do with the attack.

Pete Hoekstra, former chairman of the House intelligence committee, told FoxNews.com the attack appeared to have the markings of an Al Qaeda or Al Qaeda-affiliated strike.

"We've been talking for years about the desire of Al Qaeda, radical jihadists to celebrate the anniversary of 9/11," he said. "All my background, all of the conversations that I've had over the last 18 hours lead many people to believe that this was just more than a mere coincidence."

Hoekstra noted that the supposed protesters -- purportedly angry over a film that ridiculed Islam's Prophet Muhammad -- didn't attack in Tripoli. They attacked in Benghazi, "where it so happens our ambassador is." And they happened to be "fully armed and fully equipped," he said.

Hoekstra noted that Al Qaeda chief Ayman al-Zawahri had recently released a video calling on militants to attack Americans in revenge for the killing of an operative in Pakistan. The message said his "blood is calling on you, inciting you to fight and kill the crusaders."

Hoekstra said the film may have been just a cover to carry out such an attack.

Two intelligence officials also said the attack looked "coordinated."

London-based think tank Quilliam reached the same conclusion, saying the Benghazi strike appeared to be a "well-planned terrorist attack that would have occurred regardless of the demonstration (over the film)."

Also, the brother of Zawahri was nearby during the separate protest at the American Embassy in Cairo on Tuesday.

A few lawmakers on Capitol Hill appeared skeptical of the film explanation. "The timing of this on the eleventh anniversary of 9/11 is more than just coincidence," Sen. James Inhofe, R-Okla., said in a statement.

The FBI is investigating the attack and the deaths of American personnel. A U.S. military aircraft is expected to leave from Libya soon with the wounded and bodies of the dead aboard.

President Obama, meanwhile, condemned the "outrageous and shocking" attack Wednesday, as he and other officials vowed to "bring justice" to the killers while moving quickly to bolster security in Libya and at other diplomatic posts.

"Make no mistake. Justice will be done," Obama said, speaking from the Rose Garden alongside Secretary of State Hillary Clinton.

Obama and Clinton both condemned the killers, while stressing that the U.S. bond with the Libyan government would not suffer as a result.

"Make no mistake. We will work with the Libyan government to bring justice to killers who attack our people," Obama said, adding: "There is absolutely no justification to this type of senseless violence. None."

Stevens was killed Tuesday night when he and a group of embassy employees went to the consulate to try to evacuate staff. The protesters were firing gunshots and rocket-propelled grenades.

Obama and Clinton offered new details Wednesday about the chaotic aftermath. They said some Libyans tried to fight to defend the U.S. post while it was under attack, even carrying Stevens' body to a hospital. The Libyan doctor who treated Stevens also told The Associated Press that he died of severe asphyxiation, apparently from smoke inhalation, and that he tried for 90 minutes to revive him. There continue to be conflicting reports about the circumstances of Stevens' death.

Clinton, speaking from the State Department, called the tragedy "an attack that should shock the conscience of people of all faiths."
Obama, in a statement Wednesday morning, said he's directed the administration to provide "all necessary resources" to support security for U.S. personnel in Libya and to increase security at diplomatic offices around the world.

The White House and Congress ordered flags to be flown at half-staff in the wake of the tragedy. The House also held a moment of silence for the victims Wednesday afternoon.

The State Department identified one of the other three Americans killed as Foreign Service Information Management Officer Sean Smith, a husband and father of two who had worked for the State Department for 10 years. The U.S. government is still notifying the next of kin for the other two individuals killed, and has not identified them.

Stevens was appointed as ambassador to Libya in May 2012.

He served as a special representative to the Libyan Transitional National Council during the revolution in 2011, and as the deputy chief of mission from 2007 to 2009.

U.S. officials remain on alert for violence at other diplomatic posts.

Fox News' Catherine Herridge, Ed Henry and Bret Baier and FoxNews.com's Judson Berger and The Associated Press contributed to this report.