In a White House appearance Tuesday, Mr. Obama said the U.S. would "work with the Libyan government to bring to justice" those who Stevens and three other Americans.
White House press secretary Jay Carney said it was too early to judge whether the attack was planned.
"I know that this is being investigated, and we're working with the Libyan government to investigate the incident. I would not want to speculate on that at this time," he said. Several Libyan security guards also were killed.
Rogers, R-Mich., said U.S. intelligence had not yet determined who was responsible, but added, "Our list is narrowing."
"When you see (such an attack), it wasn't some folks who had some guns in their garage and said let's shoot up the consulate," Rogers said.
Analysts are working on several different scenarios based on intelligence that could lead to a motive for the attack. Some concern the possibility of targeting high-ranking officials, according to a law enforcement official briefed on the investigation. But none of the intelligence thus far has suggested terrorists would specifically target Stevens, said the official who also spoke on condition of anonymity because he was not authorized to speak publicly about the investigation.
The attack in Libya, which came hours after a mob stormed the U.S. Embassy in Cairo and tore down the U.S. flag, was presumed to have been triggered by a movie, whose trailer has gone viral on YouTube, depicting the Islamic prophet Muhammad in disrespectful ways. In an extraordinary move, Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, called anti-Islamic preacher Terry Jones and asked him to stop promoting the film. A spokeswoman said the church would not show the film Wednesday evening.
"Make no mistake. Justice will be done," a somber Obama pledged at the White House, Secretary of State Hillary Rodham Clinton at his side.
He ordered increased security at U.S. diplomatic missions overseas, particularly in Libya, and said he condemned "in the strongest possible terms the outrageous and shocking" attack. Clinton said she was particularly appalled that the attack took place in Benghazi, which the U.S. had helped liberate from dictator Muammar Qaddafi during the Arab Spring revolution in Libya last year.
The aftermath of the two attacks also stirred the U.S. presidential campaign, where until Wednesday, foreign policy had taken a back seat to the struggling economy.
The Republican nominee, Mitt Romney, criticized the administration for statements issued before and after the Cairo attacks that expressed sympathy for those insulted by the video. But he in turn was criticized for turning a tragedy too quickly into political fodder, and getting key details wrong.
Obamathat Romney "seems to have a tendency to shoot first and aim later."
Obama and Clinton made a rare joint visit to the State Department, where grieving colleagues of Stevens and the other three Americans killed in Benghazi gathered in a courtyard. The president also ordered U.S. flags to be flown at half-staff at government and military buildings and vessels around the world until sunset on Sept. 16. Flags had already been lowered in many places to commemorate the victims of the 9/11 attacks.
Clinton denounced those who might kill over an insulting movie.
"There is no justification for this," Clinton said. "None. Violence like this is no way to honor religion or faith and as long as there are those who would take innocent life in the name of God, the world will never know a true and lasting peace."
Underscoring the administration's frustration, Clinton wondered aloud about the attack in Benghazi, which Qaddafi had once threatened to destroy.
"This is not easy," she said. "Today, many Americans are asking, indeed I asked myself, how could this happen? How could this happen in a country we helped liberate, in a city we helped save from destruction? This question reflects just how complicated and, at times, just how confounding, the world can be."
"But we must be clear-eyed in our grief," she said, saying the attack was carried out by a "small and savage group" not representative of the Libyan people. She noted that Libyan security guards had tried to fight off the attackers, had carried Stevens' body to the hospital and led other consulate employees to safety.
Stevens, a 52-year-old career diplomat, was killed after he became separated from other American officials during the consulate attack. It's unclear when he died: He was taken by Libyans to a hospital, and his remains were delivered hours later to U.S. officials at the Benghazi airport.
"The mission that drew Chris and Sean (Smith) and their colleagues to Libya is both noble and necessary, and we and the people of Libya honor their memory by carrying it forward," Clinton said.
U.S. officials said some 50 Marines were being sent to Libya to reinforce security at U.S. diplomatic facilities.
Stevens spoke Arabic and French and had already served two tours in Libya, including running the office in Benghazi during the revolt against Gadhafi. He was confirmed as ambassador to Libya by the Senate earlier this year.