Forget Broadway. The most riveting drama on a New York stage next week will be at the United Nations, as world leaders including President Obama and Iran’s new president, Hassan Rouhani, address global audiences and test the diplomatic openings for addressing two of the world’s most explosive issues: Syria and Iran’s nuclear program.

In recent years the annual gathering of world leaders in New York for the opening of the UN General Assembly had become more of a show than a diplomatic forum – thanks in large part to Iran’s former president, Mahmoud Ahmadinejad, whose version of shock theater drew boldface headlines and wide disdain but facilitated few diplomatic overtures.

But next week things should be different. Mr. Rouhani, whose six-day visit to New York begins Sunday, will take his international charm offensive to the UN dais, where he is expected to argue that Iran is ready to reach a fair accord on its nuclear program that reassures the world about Iran’s intentions.

Mr. Obama, who only two weeks ago was threatening to unleash American military might against the regime of Syrian President Bashar al-Assad over use of chemical weapons in Syria’s civil war, is expected to hail a barely week-old US-Russia plan to rid Syria (and the world) of its substantial chemical weapons stockpile.

And Obama, who came into office in 2009 extending a diplomatic hand to Tehran, also is likely to take note of the new tone from Iran’s leadership and to hold out hope for a diplomatic resolution to Iran’s nuclear challenge, perhaps even for a new era of cooperation between the US and Iran.

Obama will underscore in his speech that the US remains open to and prefers “peaceful resolution” of the Iranian nuclear standoff, says Ben Rhodes, White House deputy national security adviser for strategic communications. But the president will also reiterate that it won’t be Iran’s rhetoric, but the steps it takes to prove the peaceful nature of its nuclear program, that the US and the international community want to see.

“We’ve always made clear we’re going to make decisions based on the actions of the Iranian government,” Mr. Rhodes says, “not on their words.”

Also next week, though on a side stage, the UN Security Council will try to deliver a stalled resolution needed to back up the Syrian chemical weapons plan. Western powers want the resolution to have the teeth to prevent Mr. Assad from dallying or backtracking on a commitment he has made to give up all of Syria’s chemical weapons. Russia has so far balked at endowing the resolution with any recourse to the use of force, fearing the US, France, and others might take that as a green light to launch military strikes against Assad.

The Security Council won’t be the only venue for Syria action. UN Secretary-General Ban Ki-moon will meet with Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov to push forward on the convening of a Syria peace conference. Mr. Ban has suggested that a successful meeting could even result in the setting of a conference date for sometime in October.

Finally, for those who crave suspense, there’s the big question that the Washington “diplomaterati” asking: Will Obama and Rouhani cross paths at the UN, and if they do, will they even (gasp) shake hands? After all, no such basic sign of mutual acknowledgement has occurred since before the Iranian Revolution of 1979.

Yet as intriguing as the prospect of a US-Iran handshake may be, the real importance of next week’s presidential speeches – Obama and Rouhani are expected to speak just a few hours apart on Tuesday – will be in the promise they hold out for a diplomatic breakthrough in the coming weeks and months.

“There’s been a lot of talk about something informal – a handshake, an exchange of greetings in a hallway – but I wouldn’t overemphasize it,” says James Walsh, a research associate at the Massachusetts Institute of Technology’s Security Studies Program. “More important is the exchange [among] diplomats,” he says, adding, “At the end of the day, it’s what the governments say that will be important.”

But Dr. Walsh, who has discussed nuclear programs with both Iranian and North Korean officials, says Rouhani, in particular in his UN speech, is likely to provide important clues concerning Iran’s approach to the nuclear standoff in the coming months.

Rouhani “has to balance messages to three communities – to the US, to the broader international community, and back home in Tehran,” Walsh says. Noting that Rouhani’s UN appearance will actually be “his first big domestic speech,” Walsh adds that Rouhani “has to walk a line by trying to signal to the international community that he wants to be conciliatory, but not appear to his domestic audience that he’s a big pushover and lapdog to the West.”

Iranians – and indeed the world – were ready for a change from the antics of Mr. Ahmadinejad, who seemed to relish being so outrageous in his UN speeches that he caused droves of diplomats to walk out of the General Assembly chamber. But Rouhani will have to be able to demonstrate quickly to his home public that his more conciliatory approach is bearing fruit, others say.

“If Rouhani’s diplomacy can’t deliver more than Ahmadinejad’s theatrics, then the [Iranian] conservatives will be back in the driver’s seat,” says Trita Parsi, president of the National Iranian American Council in Washington.

Others say it’s up to Obama and the US to meet Rouhani half-way and take advantage of what may be a short window of opportunity to work with a new tone coming out of Tehran.

“What we’re hearing from [Rouhani] is so different from what we use to hear from Ahmadinejad,” says Michael Doyle, a professor of US foreign and security policy at Columbia University in New York and a former assistant secretary general at the UN. “We really should step up and start talking with him,” he adds, “if we flub this one, it will be a long time before we get another chance to cool off the crisis with Iran.”

Of course some in the broader UN audience are deeply skeptical of Rouhani’s intentions even before he sets foot in New York.

“One should not be taken in by Rouhani’s deceptive words,” Israeli Prime Minister Benjamin Netanyahu said in a statement Friday. “The test is not Rouhani’s words, but rather the Iranian regime’s actions,” Mr. Netanyahu added, saying it would only be through a series of steps such as stopping all uranium enrichment, removing all enriched uranium, and ending the plutonium track of its nuclear program that Iran would be making “a real halt to the nuclear program.”

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And as in past years, some Iranian dissident groups are planning to demonstrate outside the UN to let Rouhani know that not everyone welcomes him.

The Association of Iranian-Americans in New York and New Jersey is planning a rally at which prominent members of the Bush administration – including former US ambassador to the UN John Bolton – will speak even as Rouhani stands at the UN podium.