Obama, in an interview with The Associated Press, acknowledged that American estimates are "more conservative" than those of the Israelis, who say it will take Iran months to reach a nuclear weapons capability.
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The president used the same timetable in March, before traveling to Israel. The United States and Israel contend that Iran's nuclear program is aimed at building a bomb, while Tehran says it is enriching uranium for peaceful purposes.
Obama also told the Associated Press that the world must "test" whether Iranian President Hassan Rohani is serious about resolving its nuclear dispute diplomatically. But he says the United States won't take a "bad deal" from Iran.
Last week, Obama spoke by phone with Rohani, marking the first direct exchange between U.S. and Iranian leaders in more than 30 years.
"Rohani has staked his position on the idea that he can improve relations with the rest of the world," Obama said. "And so far he's been saying a lot of the right things. And the question now is, can he follow through?"
But Obama said Rohani is not Iran's only "decision-maker. He's not even the ultimate decision-maker," a reference to the control wielded by Iran's supreme leader, Ayatollah Ali Khamenei.
Given the supreme leader's broad influence, some countries, most notably Israel, have questioned whether Rohani actually represents real change in Iran or just new packaging of old policies.
The president empathized with Prime Minister Benjamin Netanyahu, saying he is "understandably" very skeptical about Iran, "given the threats that they've made repeatedly against Israel, given the aid that they've given to organizations like Hezbollah and Hamas that have fired rockets into Israel."
Obama added that if he were Israel's leader, he'd be "be very wary as well of any kind of talk from the Iranians."
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