"We should hear him out but see what the actual detail is on the nuclear dossier and Iranian support on Syria. We will judge Iran on its actions, not just its words," said one diplomatic source.
Rouhani's flurry of goodwill motions comes less than a week before he is due to deliver a highly scrutinised address to the United Nations General Assembly in New York.
While his predecessor, Mahmoud Ahmadinejad, used the UN as a pulpit for inflammatory speeches railing against Israel and the US, Rouhani is expected to strike a softer note.
He will deliver the speech as Iran's economy continues to suffer under a punishing sanctions regime designed to put pressure on the few remaining buyers of Iranian oil and to choke off Tehran's access to its dwindling foreign exchange reserves.
Obama revealed last week that he had exchanged letters with his Iranian counterpart in recent weeks and Rouhani told NBC the correspondence "could be subtle and tiny steps for a very important future".
The US President said earlier this week that there was an opportunity for diplomacy over the nuclear issue and "I hope the Iranians take advantage of it".
"There are indications that Rouhani, the new President, is somebody who is looking to open dialogue with the West and with the United States in a way that we haven't seen in the past," Obama said.
While Iran has always maintained its nuclear programme was for peaceful purposes, Rouhani's public commitment not to seek nuclear weapons will be viewed as a positive step.
Earlier in the day, Sotoudeh, the human rights lawyer, said she was in "good" condition after spending three years in prison and nearly a year on hunger strike.
"Psychologically, my condition is very good but my experience - with all the psychological pressure, the tense security atmosphere, and not having access to phone calls among other things - was very tough," she said.
Sotoudeh was briefly released in January when the UN and European Union took up her case but was promptly reimprisoned. She told the AFP news agency she was confident her freedom was now permanent.
The US State Department said it welcomed the release of the political prisoners and called on Iran "to release all prisoners of conscience in its custody".
This week Ayatollah Ali Khamenei, Iran's supreme leader, said he was "not against" diplomatic outreach to the West in what analysts said could be a significant step towards ending his country's international isolation.
In a small but widely publicised gesture, Rouhani took to Twitter to wish "all Jews" a happy Rosh Hashanah, the Jewish New Year. The tweet marked a significant shift from the fiery rhetoric of Ahmadinejad, who denied the Holocaust to the fury of Jews worldwide.
The Rosh Hashanah tweet was rejected by Benjamin Netanyahu, the Israeli Prime Minister, who said: "I am not impressed by the blessings uttered by a regime that just last week threatened to destroy the state of Israel."
