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Mr. Rouhani denounced the “occupation of Palestine” by the Israelis, criticized economic sanctions against his country and blasted the U.S. for conducting drone strikes around the world, all while denying that Iran is interested in nuclear arms.

Iran seeks to resolve problems, not create them,” he said. “Iran’s nuclear program and that of all other countries must pursue exclusively peaceful purposes. I declare here openly and unambiguously that, not withstanding the positions of others, this has been and always will be the objective of the Islamic Republic of Iran. … Our national interests make it imperative that we remove any and all reasonable concerns about Iran’s peaceful nuclear program.”

The specific issue of Iran may have dominated the day, but Mr. Obama also used his address to focus on America’s broader role in the world.

He shot back at Russian President Vladimir Putin, who recently took issue with “American exceptionalism” and the U.S. willingness to strike Syria even without authorization from the United Nations.

“The danger for the world is that the United States … may disengage, creating a vacuum of leadership that no other nation is ready to fill. I believe that would be a mistake,” Mr. Obama said.

“I believe America must remain engaged for our own security. I believe the world is better for it. Some may disagree, but I believe that America is exceptional — in part because 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 interests of all,” he said.