"The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested," Obama said. Iranian President Hassan Rouhani was present and also set to address the assembly later in the afternoon.
Obama called on Iran to take "transparent" and "verifiable" actions to allay international fears over its nuclear program, which Tehran insists is for research and medical purposes.
While Obama's speech touched on many aspects of US foreign policy, it focused mainly on the Middle East, especially Iran and Syria.
"The United States is chastised for meddling in the region, and accused of having a hand in all manner of conspiracy," he said. But Obama warned that the United States was "prepared to use all elements of our power, including military force, to secure these core interests in the region."
He chided the international community on Syria, saying, "our response has not matched the scale of the challenge." Aid has fallen short and extremism has taken root, Obama said, adding that "A peace process is stillborn."
Obama once again called on the UN Security Council to press Syria on getting rid of its chemical weapons. "There must be a strong Security Council resolution to verify that the Assad regime is keeping its commitments," he said, referring to the US and Russia-backed proposal that would seek the removal and destruction of Syria's chemical weapons by mid-2014.
He also announced an additional $340 million in humanitarian aid for Syria.
"There must be consequences if they fail to do so. If we cannot agree even on this, then it will show that the United Nations is incapable of enforcing the most basic of international laws."
Turning to Egypt, Obama said, "Mohamed Morsi was democratically elected but proved unwilling or unable to govern in a way that was fully inclusive." While he said the interim government, which replaced Morsi after military intervention, was responding to the "desires of millions of Egyptians," Obama conceded that it had also made "decisions inconsistent with inclusive democracy."
Obama defended the United States' role in the world, saying, "I believe America is exceptional." He continued, "We have shown a willingness through the sacrifice of blood and treasure to stand up not only for our own narrow self interest, but for the interest of all."