Suzanne Maloney, a former State Department official, said Obama should be wary of making a bold diplomatic gesture with so much about Rouhani's intentions still unknown.
"They have to be clear that this is someone they wouldn't need to dissociate themselves from shortly after," said Maloney, now a Middle East fellow at the Brookings Institution. "When you're talking about Iran, I think that's almost impossible to do."
Anthony Cordesman, a foreign policy analyst at the Center for Strategic and International Studies, agreed that a leaders meeting does come with risks. But he urged the White House to consider the positive message it would send to Iranian moderates if Obama extended a hand to their newly elected leader.
"It's absolutely vital that you take this window of opportunity," Cordesman said. "Rebuffing Rouhani without actually listening to him is scarcely going to empower moderates in Iran."
In Tehran, meanwhile, Iran said Monday it had freed 80 prisoners arrested in political crackdowns. That could offer another diplomatic boost for the country's new president as he arrives for the U.N. meeting.
The announcement of the mass release came just hours after Hasan Rouhani departed for New York for the annual U.N. General Assembly, where he is expected to seek Western pledges to restart stalled negotiations over Iran's nuclear program.
Catherine Ashton, the EU's foreign policy
Back in Washington, senators urged Obama to reaffirm at the U.N. that, despite Rouhani's recent overtures, the U.S. will not accept a nuclear-capable Iran. In two separate letters, top Democrats and Republicans also called on the president to make clear that the U.S. will continue tough sanctions against Tehran.
"Now is not the time to let up on this pressure," Sens. Chuck Schumer, D-N.Y., and John McCain, R-Ariz., wrote in one letter to Obama. "Removal of any existing sanctions must depend on Iran's halting of its nuclear program. Conversely, the continuation or expansion of its nuclear activities will only lead to more sanctions led by the United States and our friends and allies."