Iranian President denies requesting meeting with Trump

"Not this year, nor last year," Rouhani told CNN. "We have never made such a request for a meeting with the President of the United States."

Trump started his second day at the UN General Assembly in typical fashion, with an early morning tweet. He wrote, "Despite requests, I have no plans to meet Iranian President Hassan Rouhani. Maybe someday in the future. I am sure he is an absolutely lovely man!"

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Rouhani told CNN's Christiane Amanpour that while Iran received eight requests from US officials for a meeting last year, he did not think talks between the two leaders were "appropriate," then or now.

And as for being called "a lovely man" by someone who labeled his country "the leading state sponsor of terror," Rouhani dismissed the comment, saying Trump is "playing with words and will not get us to any solutions."

Attempts to save the Iran nuclear deal

The United States and Iran have been at a standoff since Trump announced his decision to pull out of the Iran nuclear deal in May, pitting him against other signatories.

The nuclear accord was one of President Barack Obama's crowning achievements, and Trump's swift exit delivered a powerful blow to his legacy.

The rest of the deal's signatories, which include US allies Britain, France and Germany, have been scrambling to save what is known officially as the Joint Comprehensive Plan of Action. Rouhani acknowledged that together with Russia and China, the signatories have proven they want to salvage the agreement, but he said they have fallen short of expectations, and he has not seen any results in a "tangible fashion."

Jailed dual nationals in Iran

Pressed on the fate of dual nationals still jailed in Tehran's Evin Prison, Rouhani said Iran has its own citizens imprisoned in Western countries. Those jailed in Iran include British-Iranian mother and charity worker Nazanin Zaghari-Ratcliffe.

Rouhani told Amanpour that "all prisoners must be freed and returned to their families, but it must be a path that travels both ways."