Among the four killed was Chris Stevens, the first U.S. ambassador to die in an attack since 1979.
"Without people like them, America could not sustain the freedoms we enjoy, the security we demand, and the leadership that the entire world counts on," Obama said in his weekly radio and Internet address Saturday.
The theme echoed comments by the president in recent days, including at a ceremony Friday at Andrews Air Force Base marking the return of the four men's remains.
The remarks allowed Obama to emphasize his role as commander in chief less than two months before the presidential election and draw attention to foreign policy, an area where he wins more approval from voters that his rival, Mitt Romney.
Muslims angry over the film produced in the U.S. denigrating the Prophet Muhammad took the streets on Friday in more than 20 countries from the Mideast to Southeast Asia, and at least six people were killed. A day earlier, four Yemeni demonstrators were killed in protests that turned violent at the U.S. Embassy in Sanaa.
Egyptian police on Saturday cleared out protesters who have been clashing with security forces for the past four days near the U.S. Embassy. The only report Saturday of violence linked to the film came from Australia, where riot police clashed with about 200 protesters at the U.S. Consulate in Sydney.
U.S. officials say the Sept. 11 attack of the consulate in Benghazi appeared to be connected to protests elsewhere in the Arab world. U.S. investigators are trying to determine whether the strike was planned and was more than spontaneous anger over the YouTube video that denigrated the Prophet Muhammad.
Obama attempted to send a message to the protesters on the street.
"This tragic attack takes place at a time of turmoil and protest in many different countries," he said. "I have made it clear that the United States has a profound respect for people of all faiths. We stand for religious freedom. And we reject the denigration of any religion – including Islam."
But, he added: "Yet there is never any justification for violence. There is no religion that condones the targeting of innocent men and women."
He pledged to bring the attackers to justice.
"We will not waver in their pursuit," he said. "And we will never allow anyone to shake the resolve of the United States of America."
The U.S. has deployed drone surveillance, an FBI investigation team, and a small surge of U.S. intelligence officers to Libya to try to track down al-Qaida sympathizers who may have used protests of the anti-Muslim video to stage the assault on the consulate.
In addition to Stevens, also killed in Benghazi were Sean Smith, an Air Force veteran who worked as an information management specialist for the State Department; Glen A. Doherty, a former Navy SEAL who worked for a private security firm and was protecting the consulate in Benghazi; and Tyrone S. Woods, also a former Navy SEAL who had served protective duty in various U.S. posts.
In the Republican radio address, Rep. Allen West of Florida called on Obama to work with Congress to replace across-the-board spending cuts that West said were a serious threat to national security. West said automatic cuts scheduled to take effect in early January would be "deeply destructive" to the military and to core government responsibilities such as patrolling U.S. borders and air traffic control.
West, who served for 22 years in the Army, said the president has balked at efforts by congressional Republicans to replace the automatic cuts, which were imposed as part of a deficit-cutting deal agreed to by both parties.