Javad Zarif and other Iranian officials are under strict travel restrictions when they are in the US

The State Department said Saturday that it would only allow Iranian Foreign Minister Mohammad Javad Zarif to visit the country's ambassador in a US hospital if Tehran releases a detained American citizen.

"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," a State Department spokesperson told AFP.

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

Majid Takht-Ravanchi, the country's UN ambassador, is undergoing cancer treatment at a hospital in New York, where Zarif was visiting for the United Nations General Assembly.

Zarif and other Iranian officials are under strict travel restrictions when they are in the US that limit them to the area around the UN headquarters.

Tensions between Washington and Tehran have soared since last year, when US President Donald Trump quit a 2015 deal aimed at curbing Iran's nuclear program, and imposed punishing sanctions on the Islamic republic.