BENGHAZI, Libya (AP) ― The U.S. dispatched an elite group of marines to Tripoli on Wednesday after the mob attack that killed the U.S. ambassador and three other Americans. Officials were investigating whether the rampage was a backlash to an anti-Islamic video with ties to Coptic Christians or a plot to coincide with the anniversary of the 9/11 terror attacks.

Tuesday’s stunning attack on the American Consulate in Benghazi poses a daunting task for U.S. and Libyan investigators: searching for the culprits in a city rife with heavy weapons, multiple militias, armed Islamist groups and little police control.

The one-story villa that serves as the consulate was a burned-out wreck after the crowd armed with machine guns and rocket-propelled grenades rampaged through it. Slogans of “God is great” and “Muhammad is God’s Prophet” were scrawled across its scorched walls. Libyan civilians strolled freely in charred rooms with furniture and papers strewn everywhere.

President Barack Obama vowed in a Rose Garden address that the U.S. would “work with the Libyan government to bring to justice” those who killed Ambassador Chris Stevens, information manager Sean Smith and two other Americans who were not identified. Three other Americans were wounded.

Stevens was the first U.S. ambassador killed in the line of duty in 30 years.

“We reject all efforts to denigrate the religious beliefs of others, but there is absolutely no justification for this type of senseless violence. None,” said Obama, who also ordered increased security at U.S. diplomatic posts abroad.

Republican Mitt Romney accused the Obama administration of showing weakness in the consulate killings, but the president retorted that his rival “seems to have a tendency to shoot first and aim later.” Some in the Republican Party called Romney’s remarks hasty.

The mob attack on Tuesday ― the 11th anniversary of the Sept. 11, 2001, terrorist strike in the U.S. ― was initially presumed to have been a spontaneous act triggered by outrage over a movie called “Innocence of Muslims” that mocked Islam’s Prophet Muhammad that was produced in the U.S. and excerpted on YouTube. The amateurish video also drew protests in Cairo, where angry ultraconservatives climbed the U.S. Embassy’s walls, tore down an American flag and replaced it with an Islamic banner.

But a U.S. counterterrorism official said the Benghazi violence was “too coordinated or professional” to be spontaneous. The official spoke on condition of anonymity because he was not authorized to discuss the incident publicly.

The FBI was sending evidence teams to Libya, a law enforcement official said.

Libya’s new leadership ― scrambling to preserve ties with Washington after U.S. help to overthrow former dictator Moammar Gadhafi ― vowed to find those behind the attack. Interim President Mohamed Magariaf apologized to the United States for what he called the “cowardly” assault, which also killed several Libyan security guards at the consulate in the eastern city.

Parliament speaker Omar al-Houmidan suggested the attack might have been planned, saying the mob “may have had foreign loyalties” ―- an apparent reference to international terrorists. “We are not sure. Everything is possible,” he said.

A Libyan jihadist group, the Omar Abdel-Rahman Brigades, claimed responsibility for a bomb that went off outside the Benghazi consulate in June, causing no injuries. The group, which also carried out several attacks on the International Red Cross in Libya, said at the time that the bomb was revenge for the killing of al-Qaida’s No. 2, Abu Yahya al-Libi, in a U.S. drone strike in Pakistan.

About 50 U.S. Marines were sent to Libya to guard U.S. diplomatic facilities. The marines are members of an elite group known as a Fleet Antiterrorism Security Team, or FAST, whose role is to respond on short notice to terrorism threats and to reinforce security at embassies.

The marines, sent from a base in Spain, were headed initially to the U.S. Embassy in Tripoli, not to Benghazi, according to U.S. officials, who spoke on the condition of anonymity because they were not authorized to talk to the press.

The consulate attack illustrated the breakdown in security in Libya, where the government is still trying to establish authority months after Gadhafi’s fall.

There also were indications that two distinct attacks took place ― one on the consulate, then a second hours later early Wednesday on a nearby house to which the staff had been evacuated.

The crowd of several thousand that descended on the consulate was armed with machine guns and rocket-propelled grenades, said Wanis el-Sharef, the deputy interior minister of Libya’s eastern region.

A small contingent of Libyan security protecting the facility fired in the air, trying to intimidate the mob. But faced with superior size and firepower, the Libyan security withdrew, el-Sharef said. Gunmen stormed the building, looted its contents and torched it, he said.

Details of how the Americans were killed were still unclear.

Stevens, 52, and a consulate staffer who had stayed behind in the building died in the initial attack, el-Sharef said. The rest of the staff successfully evacuated to a nearby building, preparing to move to Benghazi Airport after daybreak to fly to the capital of Tripoli, he said.

Hours after the storming of the consulate, a separate group of gunmen attacked the other building, opening fire on the more than 30 Americans and Libyans inside. Two more Americans were killed, he said.

Dr. Ziad Abu Zeid, who treated Stevens, told the Associated Press that he died of asphyxiation, apparently from smoke. In a sign of the chaos, Stevens was brought by Libyans to the Benghazi Medical Center with no other Americans, and no one at the facility knew who he was, Abu Zeid said.

He said he tried to revive Stevens for about 90 minutes “with no success.” The ambassador was bleeding in his stomach because of the asphyxiation but had no other injuries, the doctor said.

Widely regarded as one of the most effective American envoys to the Arab world, Stevens brokered tribal disputes and conducted U.S. outreach efforts in Jerusalem, Cairo, Damascus and Riyadh. As a rising star in U.S. foreign policy, he retuned to Libya four months ago, determined to see a democracy rise where Gadhafi’s dictatorship flourished for four decades.

Smith, 34, was an Air Force veteran who had worked as an information management officer for 10 years in posts such as Brussels, Baghdad and Pretoria. Smith was also well-known in the video game community.

The bloodshed stunned many Libyans, especially since Stevens was a popular envoy among different factions and politicians, including Islamists, and was seen as a supporter of their uprising against Gadhafi.

The leader of Ansar al-Shariah, an armed ultraconservative Islamist group, denied any involvement in the attack.

“We never approve of killing civilians, especially those who helped us,” Youssef Jihani said in a reference to Stevens. “We are well-educated and religious.”

The violence in Libya raised worries that further protests could break out around the Muslim world, but the reaction was limited.

The movie, “Innocence of Muslims,” came to attention in Egypt after its trailer was dubbed into Arabic and posted on YouTube. The video-sharing website blocked access to it Wednesday. The trailer depicts Muhammad as a fraud, a womanizer and a madman in an overtly ridiculing way, showing him having sex and calling for massacres.

In Cairo, some 200 Islamists staged a second day of protest outside the U.S. Embassy on Wednesday, but there were no more attempts to scale the embassy walls. After nightfall, the group dwindled and some protesters scuffled with police, who fired tear gas and dispersed them, emptying the streets.

In a statement on his official Facebook page, Egypt’s Islamist president, Mohammed Morsi, condemned the movie, saying the government was responsible for protecting diplomatic missions as well as the freedom of speech and peaceful protest.

But, he added, authorities “will confront with full determination any irresponsible attempt to break the law.”

Romney’s criticism of Obama didn’t mesh completely with events in Cairo.

A U.S. Embassy statement that Romney referred to as akin to apology was issued by the Cairo embassy at midday on Tuesday at a time the staff was aware of still-peaceful demonstrations nearby. It was four or five hours later when the mob breached the compound’s walls and tried to burn a U.S. flag, and later still when the Libya attack happened.

The embassy statement condemned “the continuing efforts by misguided individuals to hurt the religious feelings of Muslims ― as we condemn efforts to offend believers of all religions,” and noted that religious freedom is a cornerstone of American democracy.

About 50 protesters burned American flags outside the U.S. Embassy in Tunisia’s capital Wednesday but were kept away from the building by reinforced security. And in Gaza City, dozens of protesters carrying swords, axes and black flags chanted “Shame on everyone who insults the prophet.” The rally was organized by supporters of a militant group aligned with the ruling Hamas movement.