New York City (CNN) The US has denied permission for Iranian Foreign Minister Javad Zarif to visit a colleague receiving treatment in a New York City hospital. But it would have been allowed if Iran released a US citizen held in detention, a US administration official tells CNN Friday.

The Iranian Foreign Minister is under tight US travel restrictions while in New York this week for the United Nations General Assembly.

"Foreign Minister Zarif would like 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. We have relayed to the Iranian mission that the travel request will be granted if Iran releases a US citizen," the official said.

CNN has reached out to the Iranian mission for an official comment. Alireza Miryousefi, the mission's press officer has also tweeted, "Travel!! It is just a few Min walk," and attached a map locating the proximity of Memorial Sloan Kettering Cancer Center's proximity to the United Nations.

Iranian diplomats have complained about difficulty of getting visas before this week's UNGA.