"All those are reports in the newspaper. They are not true," Obama said.
"They have the opportunity to re-enter the community of nations and we would welcome that. The deal we'll accept is they end their nuclear program," he continued.
In his sharpest words of the debate so far, Romney accused the president of empowering dictators and despots around the world.
"The president began what I have called an apology tour—of going to various nations in the Middle East and criticizing America. I think they looked at that and saw weakness," Romney said.
"When the president said he was going to create daylight between ourselves and Israel, they noticed that as well," he added.
Obama shot back: "Nothing Gov. Romney just said is true, starting with this notion of me apologizing. ... The strength that we have shown in Iran is shown by the fact that we've been able to mobilize the world."
Romney countered with emphasis on a potential nuclear weapons threat. "We're four years closer to a nuclear Iran," he said.
"The reason I call it an apology tour," he added, "is because you went to the Middle East and you flew to Egypt and to Saudi Arabia and to Turkey and Iraq. And by the way, you skipped Israel, our closest friend in the region."