"While passions and politics can often obscure the hard work before us, let's be clear about what this moment demands," the president said. "We are at war."
"We are at war against al Qaeda, a far-reaching network of violence and hatred that attacked us on 9/11, that killed nearly 3,000 innocent people, and that is plotting to strike us again," he continued. "And we will do whatever it takes to defeat them."
Special Report: The Christmas Day Terror Attack
The president said America has "made progress" in that war, having inflicted "major blows against al Qaeda leaders." He said "we have disrupted plots at home and abroad and saved American lives."
He then reached out to the Muslim world, as he has in the past.
"We know that the vast majority of Muslims reject al Qaeda," he said. "But it is clear that al Qaeda increasingly seeks to recruit individuals without known terrorist affiliations, not just in the Middle East but in Africa and other places, to do their bidding."
Summary of White House Review
Directive from President Obama
America, he said, believes in the aspirations that all people share, such as "to get an education, to work with dignity, to live in peace and security."
"That's the vision that is far more powerful than the hatred of these violent extremists," he said.
The president went on to say that while America will strengthen its defenses, "we will not succumb to a siege mentality that sacrifices the open society and liberties and values that we cherish as Americans, because great and proud nations don't hunker down and hide behind walls of suspicion and mistrust."
"That is exactly what our adversaries want," he said. "And so long as I am president, we will never hand them that victory."
More on Obama's Remarks and the Report:
Obama Commands Intel Community to Do Better
John Brennan: I Told Leiter to Take Leave
Brennan: Yemen's Al Qaeda Is "Lethal" and "Concerning"
Transcript: Obama on Intelligence Failures
Full Obama Video
Analysis from CBS News' Bob Schieffer and Bob Orr