The United Nations General Assembly will meet in New York this week, but President Rouhani said “there is no such program for a meeting” with Trump in an interview with NBC News.
The UN summit comes after Trump doubled down on his decision to withdraw from the Joint Comprehensive Plan of Action and re-impose crippling economic sanctions on Iran.
Trump is expected to take a hard line with Iran at this session and id likely to try to persuade others to follow him in penalising the state for its nuclear activity and support of terrorism.
The Iran deal has continued support from the remaining members, most of whom are European.
France in particular expressed a strong objection to the US’s decision to abandon the painstakingly-assorted agreement.
Further US sanctions are due to take effect in November.
President Rouhani said Trump would need to rebuild the bridge he burned when he decided to drop out of the deal before any talks could be had between the men.
He said: “Naturally, if someone is keen on having a meeting and holding a dialogue and creating progress in relationships, that person would not use the tool of sanctions and threats to bear all of its power against another government and nation.
“That means that the necessary willpower is absent in order to resolve outstanding issues.”
He admitted the economic sanctions had already affected Iran’s economy for the worse, but asserted they could cope if further punishment was piled on by Trump.
Experts from Oxford Economics said in August they expected oil sanctions, that are to come into effect in November, to send the Iranian economy into recession.
However, President Rouhani believes these are empty threats.
He said: “The United States is not capable of bringing our oil exports to zero. It’s a threat that is empty of credibility.
“Perhaps on this path, we will sustain pressures but certainly the United States will not reach this objective.”