President Barack Obama pledged in a speech to world leaders Tuesday that the United States will do what it takes to prevent Iran from building a nuclear weapon and warned that time for a diplomatic resolution “is not unlimited.”

While there is still a chance to negotiate, Obama told the annual meeting of the United Nations General Assembly in New York, a nuclear-armed Iran would imperil Israel, ignite a regional arms race and destabilize the global economy.

“Make no mistake: A nuclear-armed Iran is not a challenge that can be contained,” Obama said in a speech aimed at two distinct audiences: Mideast leaders, including those of new governments emerging from the Arab Spring, and U.S. voters who in six weeks choose between him and Republican Mitt Romney in the presidential election. “The United States will do what we must to prevent Iran from obtaining a nuclear weapon.”

The Middle East and North Africa were the focus for Obama in his U.N. speech, and he used the bulk of the address to talk about the attacks on U.S. diplomatic outposts triggered by an anti-Islam video made in the U.S. The deadliest was a Sept. 11 assault on the U.S. consulate in Benghazi, Libya, that killed Ambassador Chris Stevens and three other Americans.

The violence has opened a line of attack by Romney on Obama’s foreign policy, particularly his handling of relations with Israel and the threat posed by Iran’s nuclear ambitions. In an address to the Clinton Global Initiative in New York just before Obama spoke, Romney said the U.S. seems “at the mercy of events rather than shaping events.”

At the U.N., Obama called the assaults in Libya “attacks on America” and vowed that the U.S. would be “relentless” in tracking down the killers.

While calling the video “crude and disgusting” and saying the U.S. government had nothing to do with it, Obama said such expression can’t be banned in a free society.

“Americans have fought and died around the globe to protect the right of all people to express their views — even views that we disagree with,” Obama said. “We do so not because we support hateful speech, but because our founders understood that without such protections, the capacity of each individual to express their own views, and practice their own faith, may be threatened.”

In an otherwise somber speech, Obama drew some laughter from his audience with a self-reflective defense of free speech. “Here, in the United States, countless publications provoke offense,” he said, and as president “I accept that people are going to call me awful things every day, and I will always defend their right to do so.”

He warned that newly elected leaders in countries that were swept by the Arab Spring uprising are threatened by the same anger and extremism now aimed at the U.S.

“The impulse towards intolerance and violence may initially be focused on the West, but over time it cannot be contained,” Obama said. “The same impulses toward extremism are used to justify war between Sunnis and Shia, between tribes and clans.”

While saying the future must not belong to those who slander Islam, Obama said, “Those who condemn that slander must also condemn the hate we see when the image of Jesus Christ is desecrated, churches are destroyed, or the Holocaust is denied.”

Obama restated his call that the regime of Syria’s Bashar Assad “must come to an end.”

Romney also touched on the violence in the Muslim world in his speech at the Clinton Global Initiative, repeating a line of attack against Obama that he’s been using this week in campaign appearances.

“Syria has witnessed the killing of tens of thousands of people,” he said. “The president of Egypt is a member of the Muslim Brotherhood. Our ambassador to Libya was assassinated in a terrorist attack. Iran is moving toward nuclear weapons capability. We somehow feel that we are at the mercy of events, rather than shaping events.”

Obama also addressed the conference, as will Egyptian President Mohammed Morsi and Libya’s Mohammed Yussef Magariaf, whose new governments are being tested by the turmoil.

In his remarks to the annual conference organized by former President Bill Clinton, Obama emphasized work to curb human trafficking.

Obama focused his address to the Clinton Global Initiative on his administration’s efforts to curb human trafficking. He announced an executive order strengthening prohibitions against U.S. tax dollars supporting human trafficking through contracts and more investigations into such crimes in the U.S. and abroad.

Human trafficking “must be called by its true name, modern slavery,” Obama said. He said his message to oppressed people around the world is: “We see you, we hear you, we insist on your dignity.”

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With assistance from Indira A.R. Lakshmanan and Flavia Krause-Jackson.