Mr Rouhani made his appeal for a "nuclear weapon-free world" hours before the Iranian foreign minister was due to hold crucial talks with his counterparts from six world powers, including John Kerry, the US Secretary of State.
The meeting would be the first face-to-face contact between US and Iranian foreign ministers since a cursory encounter between the two holders of those posts in 2007. It marks the opening of a bid to turn the warmer atmosphere between Iran and the US into an agreement that would settle the dispute over Iran's nuclear programme which has seen the country subjected to crippling sanctions.
Mr Rouhani says that he wants a deal in a matter of "months", but critics say that his real aim is to buy time for his country to develop the ability to make a nuclear weapon. On Thursday, he joined a debate on a nuclear-free world at the General Assembly in New York, saying: "nuclear disarmament remains our highest priority", adding: "There are no right hands for these wrong weapons."
At the very least, they want any deal that included enrichment to be conditional on Mr Rouhani admitting to the (IAEA) that Iran has tried to develop the technology for a weapon. "Giving Iran legal access to the nuclear fuel cycle is fundamentally unacceptable," said Mark Dubowitz of the Foundation for Defence of Democracies, a think-tank which has advised the Obama administration on sanctions and argued for a tough line against Tehran.
"There is no nuclear safeguards arrangement in the world that can stop a regime that is truly dedicated to the pursuit of a nuclear weapon," he added.