Obama delivered a speech Tuesday at the U.N. General Assembly, and Rouhani is scheduled to as well. But it's unclear whether the two presidents will meet.
Ben Rhodes, a White House deputy national security adviser, said Monday that no meeting has been scheduled with Rouhani for this week, but the White House remains open to diplomacy that serves American interests.
Elliott Abrams, a senior fellow at the Council on Foreign Relations, said Obama shouldn't meet with Rouhani during the U.N. gathering, though shaking hands in a corridor would be appropriate.
Abrams says that's because while Rouhani is Iran's president, he is not the country's leader. Ayatollah Ali Khamenei is the supreme leader of Iran.
"They are not counterparts, they are not equal," said Abrams, who also supervised U.S. policy in the Middle East under former President George W. Bush. "So for the president to meet with him, I think confers too great a recognition on him."
Abrams said Rouhani was a skilled political tactician when he was the country's chief nuclear negotiator from 2003 to 2005.
"Remember this is the guy -- Rouhani -- who wrote several years ago with pride how he tied us up in negotiations while the nuclear program (of Iran) was going forward," Abrams said. "So we should approach this with skepticism."
Asked Monday whether the two presidents may just shake hands, Rhodes replied, "I don't think anything will happen by happenstance on a relationship this important."
White House weighs in
The Obama administration has welcomed Rouhani's published column.
"But the fact of the matter is actions are what are going to be determinative here," White House spokesman Josh Earnest said. "The Iranians, for a number of years now, have been unwilling to live up to their obligations to the international community as it relates to their nuclear program."
The international community's economic sanctions against Iran has "taken a significant toll on their economy and put pressure on them to come back to the bargaining table," Earnest said.
He did acknowledge that Rouhani now enjoys a window of opportunity against his hard-line adversaries at home, but Iran must "demonstrate their seriousness of purpose" and show "their nuclear program is for exclusively peaceful means."
For now, Obama's schedule this week doesn't contain any meetings with Rouhani.
Asked if the United States is willing to ease sanctions against Iran, Earnest said such economic pressure "is what has brought the Iranians to the table."
Optimism in Tehran
On the streets of Iran's capital, many appear to be hopeful that their president's overtures toward the United States are a good sign. But they're also realistic that 34 years of mistrust will not disappear overnight.
"I am 99% sure things will be better," said Tehran resident Syed Ali Akbar. "I can just feel it."
Barber Hassan Ahmadi said he wants sanctions to end.
"I want to see better relations," he said, "so we can live a little easier."