But all eyes will be on Hassan Rouhani, the centrist cleric who was elected as Iran's new president in June, when he steps onto the world stage at this year's gathering in New York later this month.
Known as "the diplomatic sheikh" in his homeland, Rouhani has hinted that he favors a more conciliatory approach than his predecessor.
"The Iranian people voted 'yes' to moderation," Rouhani said during his swearing-in address. Amid the long-simmering nuclear standoff, he has also called for better relations with the West and said that the only way to get Iran out of its current rut was to negotiate with America.
A recent visit to Tehran by Jeffrey Feltman, a U.N. envoy who served as a senior State Department official during President Barack Obama’s first term, has also triggered speculation that diplomatic back channels are being explored.
Suzanne Maloney, a senior fellow with the Brookings Institution, said a thaw in relations appeared possible.
“I think this is probably the most opportune moment for genuine improvement for U.S., Iranian relations in the past three decades,” she said.
Rouhani would not be allowed to make these apparent overtures without the blessing of Supreme Leader Ayatollah Ali Khamenei, the highest-ranking political figure in the Islamic republic, according to Maloney.
“Rouhani was permitted to run by a system that recognized that it could not afford another four years or eight years of defiance and pugnacious rhetoric from a president,” she said. “It needed a fixer and Rouhani is intended to be that fixer."
With inflation running at more than 35 percent and Iran's currency rapidly depreciating, U.N. and unilateral Western sanctions have hit Iran hard. The country refuses to halt uranium enrichment, a process that can be used to build nuclear weapons, and insists the program is aimed at generating electricity and producing treatments for cancer patients.
In his first presidential address, Rouhani stated "there is the political will" to end the nuclear dispute.
Professor Nicholas Burns, a former lead U.S. negotiator on Iran’s nuclear program, said the chance to open negotiations should be welcomed by President Barack Obama, but suggested direct talks between the two countries were unlikely in the near future.
“I think they might start with negotiations with the U.N. Security Council, which puts all the right people at the table like China, Russia and Britain," he said. "If they went well, then at some point you might hope for the U.S. and Iran to have bilateral talks, but I would not expect them to happen quickly."
Burns, a former U.S. ambassador to NATO who now teaches at Harvard University’s Kennedy School of Government, added that Iran needed to back up any promises with action.
“It’s never a good idea to have a complete isolation between two countries, especially adversaries. And the United States and Iran are certainly adversaries,” Burns said.
Lord Norman Lamont, a former U.K. treasury chief, who now chairs the British Iranian Chamber of Commerce, said both sides need to be prepared to give if any talks were to succeed.
“I’m not an apologist for Iran,” he said. “I think they have many faults to answer for. The problem is each side wants the other to move and that is the difficulty. Something the West finds difficult to understand is the Iranian idea that they should be treated with courtesy and as an equal, rather than being told what to do."
Analysts have also noted that Rouhani's Cabinet includes Mohammad Javad Zarif as foreign minister. Zarif studied at San Francisco State University and the University of Denver, speaks fluent English and served as Tehran's ambassador to the U.N. from 2002-2007.
On Thursday, Zarif tweeted a "Happy Rosh Hashana" message to Jews and then distanced himself from Ahmadinejad's views on the Holocaust in a Twitter exchange with Christine Pelosi, the daughter of Rep. Nancy Pelosi, D-Calif.
Ahmadinejad had been quoted as describing the Nazi Holocaust as "a myth" while in office. In 2009, he dropped language from a speech at a U.N. conference on racism that branded the Holocaust "ambiguous and dubious."
Rouhani, who boasts a Ph.D. from a Scottish university, was the only non-conservative in the field during the election to replace Ahmadinejad. He got more than 18 million votes while five conservative candidates combined garnered just under 18 million.
Since then, he has called for Iran's government and powerful clergy to end interference in the private lives of the country's people, restore free Internet access and allow state media to be more open about Iran's problems.
Despite such overtures, the crisis in Syria could prove to be a major stumbling block to any talks between Tehran and Washington, particularly if the U.S. launches strikes against Bashar Assad's regime.
The decades-old relationship between the two countries and the fact that Syria was Iran’s only ally during its conflict with Iraq still holds tremendous resonance in Iran, Brookings Institution's Maloney said.
“Rouhani cannot help but understand that Syria is a real sinkhole for Iran,” she said. “They’ve been hedging themselves on Assad, but they are unlikely to disavow him entirely.”
Dr. Hooshang Amirahmadi, president of the American Iranian Council, questioned how much Rouhani would be able to accomplish during his term, no matter what message he delivers to the U.N. General Assembly, which opens on Sept. 17.
"You have to remember that he got barely 50 percent of the vote," he said. "So his enemies within Iran have not gone away and he hardly has a mandate to negotiate. So you will have to be realistic about what he can achieve. There are certain things that he controls, and certain things that he doesn't, so you have to be realistic. Change of government in Iran doesn't make much difference."
The Associated Press contributed to this report.