UNITED NATIONS (CNN) -- Will they or won't they?

The key question at Tuesday's opening of the U.N. General Assembly was whether U.S. President Barack Obama and Iranian President Hassan Rouhani would change years of diplomatic animosity by meeting in person, even if just for a handshake.

Both leaders were speaking on the first day of the annual gathering of world leaders in New York, and Obama made clear in his morning remarks that the United States was committed to preventing Iran from developing a nuclear weapon.

"We will not tolerate the development or use of weapons of mass destruction," he said.

At the same time, Obama welcomed what he called positive signals from Iran that it was ready to negotiate with the international community on how it can develop a peaceful use of nuclear power without creating any weapons.

"We are not seeking regime change, and we respect the right of the Iranian people to access peaceful nuclear energy," Obama said. "Instead, we insist that the Iranian government meet its responsibilities under the Nuclear Non-Proliferation Treaty and U.N. Security Council resolutions."

He noted that Iranian Supreme Leader Ayatollah Ali Khamenei issued a fatwa against the development of nuclear weapons, and Rouhani "just recently reiterated that the Islamic Republic will never develop a nuclear weapon."

"These statements made by our respective governments should offer the basis for a meaningful agreement," Obama said, adding that "to succeed, conciliatory words will have to be matched by actions that are transparent and verifiable."

Whether Obama and Rouhani would meet on the sidelines of the gathering remained uncertain.

A senior U.S. administration official said Tuesday the White House has "left the door open" to some kind of face-to-face interaction between the presidents.

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," Rhodes said.

Secretary of State John Kerry will be meeting with his 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 chance 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.

"The roadblocks may prove to be too great, but I firmly believe the diplomatic path must be tested,"Obama said.

Syria a point of contention

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.

Syria is under U.S.-led pressure to give up its chemical weapons arsenal in the aftermath of the August 21 attack on suburban Damascus that Washington and its allies blame on the al-Assad regime.

Obama said Tuesday that Syria's use of chemical weapons tested the relevance of the United Nations in the modern world, and he rejected contentions by the al-Assad regime and its main ally, Russia, that rebel forces were responsible for the attack.

"It is an insult to human reason -- and to the legitimacy of this institution -- to suggest that anyone other than the regime carried out this attack," Obama said.

Russia has blocked U.S. efforts to secure a strong Security Council resolution authorizing possible military force if Syria fails to comply with international regulations on turning over its chemical stockpiles. Obama argued Tuesday that such a resolution was vital.

"There must be a strong Security Council resolution to verify that the Assad regime is keeping its commitments, and there must be consequences if they fail to do so," he said. "If we cannot agree even on this, then it will show that the U.N. is incapable of enforcing the most basic of international laws. On the other hand, if we succeed, it will send a powerful message that the use of chemical weapons has no place in the 21st century, and that this body means what it says."

In his remarks to open the General Assembly on Tuesday, U.N. Secretary-General Ban Ki-moon called for the Syrian government to "fully and quickly" honor its obligations under the Chemical Weapons Convention, which calls for turning over control of its stockpiles.

At the same time, Ban appealed for all sides to stop supplying any weapons to all parties in the Syrian civil war while urging both the Syrian government and the opposition to respect international humanitarian law.

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.