United Nations (CNN) -- For years it was a United Nations General Assembly annual ritual: Iran's president would denounce the United States, and the American president would fire back. But this year the talks in New York are brimming with the possibility of diplomacy.
A meeting has not been scheduled between U.S. President Barack Obama and Iranian President Hassan Rouhani, both of whom will speak Tuesday before the General Assembly. Both sides, however, remain open to possibilities.
A senior administration official Tuesday said the White House has "left the door open" to some kind of face-to-face interaction between the presidents. Obama will focus on U.S. policy toward the Middle East and North Africa in his speech, a White House official said.
"We are open to engagement with the Iranian government at a variety of levels," Deputy National Security Adviser Ben Rhodes said Monday. "Provided that they will follow through on their commitments to address the international community's concerns over their nuclear program."
In lieu of a full-blown meeting, could there be a chance handshake between the leaders? "I don't think that anything would happen by happenstance on a relationship and an issue that is this important," said Rhodes.
Secretary of State John Kerry, however, will be meeting with Iranian counterpart, Foreign Minister Mohammad-Javad Zarif, at a Thursday meeting of the five permanent members of the U.N. Security Council, plus Germany. Discussions will surround restarting talks on Iran's nuclear program.
One European Union official expressed optimism over the chances for concrete progress.
"In terms of whether we're on the verge of a breakthrough, I would put it like this: I was struck as I said by the energy and determination the foreign minister demonstrated to me," said Catherine Ashton, high representative for foreign affairs and security policy of the European Union.
But no one is expecting an overnight solution to halting Iran's effort to build a nuclear weapon, an effort Tehran denies, instead insisting its nuclear program is for peaceful purposes.
"Clearly, this is going to take time. You're not going to solve all the issues with Iran in any one meeting or encounter," said Rhodes.
Iran's recent overtures signaling cooperation, though, likely stop at the topic of Syria. Iran is Syria's closest ally in the region.
"There are a lot of signs to suggest Iran is preparing for a nuclear compromise, but there are few signs to suggest that Iran is preparing to cut loose (Syrian President) Bashar al-Assad," said Karim Sadjadpour, an expert on Iran at the Carnegie Endowment for International Peace.
Al-Assad hinted at potential trouble for chemical weapons inspectors coming into the country, saying other countries may order terrorists to attack them.
"Those militants might want to stop experts' arrival. We know that those terrorists are under the control of some countries," he said in an interview Sunday with Chinese television. "And those countries may encourage the terrorists to stop experts from arrival, so that they could accuse the Syrian government for violating the agreement."
Despite al-Assad's veiled threat, positive progress has been made on the Syrian chemical weapons deal brokered by the United States and Russia in Geneva. Over the weekend, the United States said it was pleasantly surprised by the extent of Syria's initial declaration of its chemical weapons stockpile reported to the Organisation for the Prohibition of Chemical Weapons.
The United States is pushing for a U.N. Security Council resolution this week in New York to enforce the Geneva deal.