Obama also focused on the fight against militants in the Middle East, emphasizing that "America will not base our entire foreign policy on reacting to terrorism."
United States and its Arab allies began bombing Islamic State targets in Syria on Tuesday. This marked the first time that American-led action against the militant group, which is also known as ISIS or ISIL, has extended beyond Iraq. The airstrikes continued into Wednesday.
After initial hesitation to take on the group, the president has increasingly called for a group of allies to "degrade and destroy" ISIS.
Read MoreAirstrikes in Syria hit Islamic State at Iraqi border
In his speech, Obama called for the international community to address the rise of terrorism in four areas. destroy ISIS, explicitly reject the philosophy of violent religious extremism, stem the cycle of sectarian conflict and focus on creating opportunities for the young.
"No God condones this terror. No grievance justifies these actions. There can be no reasoning—no negotiation—with this brand of evil," Obama said. "The only language understood by killers like this is the language of force. So the United States of America will work with a broad coalition to dismantle this network of death."
Looking toward a long fight against extremism in the Middle East, Obama pledged to "neither tolerate terrorist safe-havens, nor act as an occupying power."
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But America will act to pursue freedom and peace throughout the world, the president insisted, and it will do so without being "distracted or deterred from what must be done."
Later on Wednesday, Obama presided over a Security Council meeting to pass a resolution to fight the threat of ISIS. Despite the unanimous passage, the president underscored that its words must be more than symbolic.
"Resolutions alone will not be enough. Promises on paper cannot keep us safe. Lofty rhetoric and good intentions will not stop a single terrorist attack," Obama said.