"Make no mistake: a nuclear-armed Iran is not a challenge that can be contained," Obama said. "It would threaten the elimination of Israel, the security of Gulf nations, and the stability of the global economy.
It risks triggering a nuclear-arms race in the region, and the unraveling of the non-proliferation treaty.
That's why a coalition of countries is holding the Iranian government accountable. And that's why the United States will do what we must to prevent Iran from obtaining a nuclear weapon."
The president reiterated that he wants to resolve the issue "through diplomacy" but the time for doing so "is not unlimited."
Obama has been under fire for, so far, opting not to meet in New York with visiting Israeli Prime Minister Benjamin Netanyahu, whose prime area of international concern is Iran's nuclear program. Obama also has not scheduled one-on-one meetings with any world leader at the U.N.
Obama began his address to the General Assembly Tuesday with a tribute to Ambassador Chris Stevens. Recalling Stevens' time serving in the Peace Corps as an English instructor in Morocco, he said Stevens "came to love and respect" the people of the region and carried that commitment throughout his life.
But he said the recent violence and unrest is indicative of the difficulties along the way. "True democracy -- real freedom -- is hard work," he said.
Obama said leaders in the region are at a critical juncture, and urged them to choose the forces of hope over the forces of intolerance.
"It is time to leave the call of violence and the politics of division behind," Obama said. "On so many issues, we face a choice between the promise of the future, or the prisons of the past. And we cannot afford to get it wrong. We must seize this moment. And America stands ready to work with all who are willing to embrace a better future."
The president called on world leaders to "marginalize" those that stoke hatred of the West in order to further their own politics.
Obama stressed that while he condemns the "crude and disgusting" video, America maintains the right to free speech.
"And on this we must agree: There is no speech that justifies mindless violence," Obama said.