For a weakened but still ambitious President Obama, the biggest foreign-policy opportunity and danger of his presidency rolls into New York next week with the arrival of Iranian leader Hassan Rouhani.

The Iranians have been signaling through various channels that they are ready to discuss a broad security framework — one that would limit Iran’s nuclear program short of producing weapons but also recognize the country’s interests in Syria and other parts of the Middle East.

A comprehensive framework appeals to prominent U.S. strategists. But it deeply worries regional players in Israel, Saudi Arabia and the United Arab Emirates, who fear their interests would be sacrificed in the grand design of the U.S.-Iranian condominium. A key test will be whether Iran demonstrates that it is ready to play a constructive role in Syria if it’s included in talks in Geneva, sponsored by the United States and Russia, about a political transition.

Here’s the way the White House is assessing the diplomatic maneuvers that will begin with Rouhani’s address to the U.N. General Assembly on Tuesday:

●U.S. officials see Rouhani as a stronger leader than his fiery predecessor, Mahmoud Ahmadinejad, as well as a more moderate one. He was elected with a mandate from the Iranian people to pursue more moderate foreign policies and to end the sanctions that are choking the Iranian economy. Though he was initially opposed by Ayatollah Ali Khamenei, Iran’s supreme leader, Rouhani now appears to have his backing, given Khamenei’s call this week for “heroic flexibility” in negotiations.

●Rouhani has signaled that he’s interested in a nuclear deal. He responded favorably to a private letter from Obama that urged bilateral U.S.-Iranian negotiations, characterizing the message as “positive and constructive” in an interview Wednesday with NBC News. U.S. officials are waiting to see how far Rouhani will go: They want more flexibility on such issues as safeguards and inspections, a greater willingness to restrict Iran’s stockpile of 20 percent enriched uranium and perhaps cap its new production at 5 percent. They also see hints of Iranian flexibility on closing the big underground facility at Fordow, outside Qom. In return, Iran clearly wants acceptance of its right to enrich uranium — something Israel opposes.

●The White House sees an opportunity in Rouhani’s designation of Foreign Minister Javad Zarif as the chief negotiator on the nuclear issue. Zarif, Iran’s former U.N. ambassador, will stay on in New York for an extra week after Rouhani’s visit. U.S. officials might start initial quiet contacts with Zarif during his trip. But officials caution that any nuclear deal must be ratified by the so-called P5+1 group, which includes Russia and China, because it would require international monitoring.

●The most urgent issue is Syria — and Iran’s possible role at a Geneva conference to negotiate a political transition from President Bashar al-Assad. U.S. officials were encouraged by Rouhani’s statement that Iran would accept whomever the Syrian people chose as president, but that’s identical to the formula Ahmadinejad offered last year. U.S. officials are waiting for evidence that Iran will back a real transition away from Assad, and that it will limit the future military role of Hezbollah in both Syria and Lebanon.

Obama concluded this month that he needed Russian help to resolve the Syria problem, and he may make a similar decision about Iran. But U.S. officials wonder whether Rouhani can make policy independent of the Quds Force of the Revolutionary Guard Corps, which has been Tehran’s covert-action arm in Syria, Lebanon, Bahrain and elsewhere. A deal with Rouhani that isn’t fully backed by Quds Force leader Qassem Suleimani would be a dangerous delusion.

The opportunity for a breakthrough with Iran after 34 years of isolation is tantalizing for Obama and his foreign-policy team. It’s the sort of big idea that conjures up visions of a new regional order that reconciles the rising revolutionary powers with the status-quo powers, much as the Congress of Vienna did for Europe in 1815. One huge benefit is that a new security framework might check the Sunni-Shiite sectarian war that is ripping apart Syria and Iraq and straining Lebanon and Bahrain.

But for a wounded Obama who lacks a solid, bipartisan foreign-policy consensus, these are giant steps. Israel appears willing to allow more time for diplomacy. But will Saudi Arabia and the Gulf nations stop fulminating about the Iranian menace long enough to consider the shape of a deal? For a battered White House, it’s a time to think big — but mind the vexing little details.

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