issue is whether both countries are ready to get into a direct bilateral discussion.
The United States suspects Iran of using its civilian nuclear program as a cover to develop atomic weapons, something it sees as a threat to Israel and to oil-producing US allies in the Gulf. Iran denies that, saying its nuclear program is for purely peaceful purposes.
A decade of negotiations between Iran and the West has yet to resolve the dispute and the United States has said it would not take any option off the table - code for a possible military strike - in dealing with Iran's nuclear program.
Speeches by Obama and Hassan Rowhani, who address the United Nations next Tuesday, will attract scrutiny for signs of a thaw. Another closely watched address will be that of Prime Minister Benjamin Netanyahu, who views a potential Iranian bomb as an existential threat to Israel and is wary of Iran's new tone.
Hassan Rowhani may extend what many analysts regard as a charm offensive by distancing himself from remarks by his predecessor, Mahmoud Ahmadinejad, who was widely vilified in the West for doubting the Holocaust and questioning Israel's right to exist.
Obama's speech must strike a balance, analysts said, between showing a readiness to engage Iran - a message he conveyed in his first week as president in 2009 by saying he would extend a hand if they would "unclench their fist" - and stressing that talks could not be endless and Iran must curb to its nuclear program.
In so doing, Obama needs to keep the door open to talks while protecting himself from attacks from conservatives who may regard his willingness to talk as weakness, particularly after his recent decision not to bomb Syria.
Elliott Abrams, who served under former Republican President George W. Bush and is now at the Council on Foreign Relations think tank, said Obama was right to test whether Iran was willing to negotiate but should avoid an encounter with Hassan Rowhani himself.
Saying the two are not equals because Hassan Rowhani serves under Iranian Supreme Leader Ali Khamenei, Abrams said: "Such a meeting is likely to be