Iran's foreign minister will be able to visit the ailing UN ambassador at a New York hospital, the US said on Saturday, but only if an American jailed in Tehran is released.

Foreign Minister Mohammed Javad Zarif is currently in New York for the annual UN General Assembly.

He had hoped to visit his country's UN Ambassador Majid Takht Ravanchi as he is being treated for cancer.

Rouhani requested permission from the State Department to see the ambassador, but the foreign minister is under sanctions severely limiting his movements in the New York.

The State Department confirmed Friday that the Iranian foreign minister wants to visit "a colleague who is in the hospital receiving world class care".

"Iran has wrongfully detained several US citizens for years, to the pain of their families and friends they cannot freely visit," the State Department said.

"We have relayed to the Iranian Mission that the travel request will be granted if Iran releases a US citizen."

Iranian President Hassan Rouhani has said that it's America's turn to release an Iranian citizen, saying that the Trump administration had said that if at least one American was freed by Iran, then Washington would reciprocate.

He said that Iran in June released Nizar Zakka, a Lebanese and permanent US resident detained in 2015 and sentenced to 10 years in prison on accusations of spying for the US.

"They only thanked Iran," Rouhani said. "The ball stands in America's court."

Iran has detained a number of foreign and dual national visitors to the country, with some countries accusing Tehran of holding them ransom.