Update at 3:07 p.m. ET. Leaders Will Not Meet:

After intense speculation that the United States and Iran were on the verge of making history today by coordinating a meeting between President Obama and new Iranian President Hassan Rouhani, there came word this afternoon that the two would not meet during the ceremonies surrounding the opening session of the U.N. General Assembly.

According to a White House pool reporter, senior administration officials said, "the White House had offered to have 'an encounter' on the sidelines of UNGA with Iranian President Rouhani, but the Iranians informed the U.S. today that it is 'too complicated for Iranians to do at this point.'"

The leaders of the two countries have not met since before the 1979 Iranian Revolution.

Obama made news during his address in front of General Assembly, when he announced that he had instructed Secretary of State John Kerry to pursue a deal with Iran over its nuclear ambitions.

Relations between U.S. and Iran have been strained over what the U.S. says is the country's march toward making a nuclear weapon. Iran has always maintained that its nuclear program is for peaceful purposes.

Our Original Post Continues:

The question of the day isn't what President Obama will speak about when he addresses the opening session of the U.N. General Assembly shortly after 10 a.m. ET.

Among the subjects he'll address are some rather obvious topics: the crisis in Syria, the Middle East peace process, the terrorist attack on a mall in Kenya, and the West's relations with Iran.

No, the big question is whether Obama and new Iranian President Hassan Rouhani will cross paths and possibly even exchange words or a handshake.

As NPR's Ari Shapiro said on Morning Edition, it would be "huge" if that happens because the leaders of the U.S. and Iran haven't met since before the 1979 Iranian Revolution. The White House, Ari added, has been "very coy" about whether Obama will see Rouhani.

Ari noted that when a White House spokesman was asked whether the two leaders might encounter each other by happenstance, the official said no such thing "would happen by happenstance."

So, if Obama and Rouhani — who have exchanged letters — do exchange greetings, we should assume it wasn't an accidental meeting and was meant to signal that relations between their two nations might be improving.

Also on Morning Edition, NPR's Michele Kelemen previewed Rouhani's address to the General Assembly. As she said, diplomats are "cautiously optimistic" about the moderate-wounding Rouhani and the prospects for negotiations about Iran's nuclear ambitions.

Rouhani is scheduled to address the General Assembly at mid-afternoon Tuesday. A rough agenda with the order of speakers is here. We'll be posting highlights of the two presidents' addresses and other leaders' speeches.

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