WASHINGTON (Reuters) - The United States has turned down a request from Iranian Foreign Minister Mohammad Javad Zarif to visit his country's ambassador to the United Nations at a New York hospital where he is being treated for cancer, the US State Department and the UN mission said on Friday.

A State Department spokesman said Zarif's request would be accepted if Iran freed one of the Americans it was holding.

In July, the United States imposed severe travel restrictions on Zarif before a UN visit this month, as well as Iranian diplomats and their families in New York, in what Zarif called "inhumane".

Zarif and Iranian diplomats are only allowed to travel in a small area of ​​Manhattan and Queens, and to and from John F. Kennedy Airport. Otherwise, they must obtain prior approval from Washington.

Iran's ambassador, Majeed Takht Rawanji, is being treated for cancer at a nearby hospital in the Upper East Side suburb of Manhattan, spokesman Ali Reza Mir Yousafi said. Zarif is in New York to attend the UN General Assembly.

"Iran has been unjustly holding several US citizens for years, and their families and friends cannot afford to visit freely," a State Department spokesman said.

"We have informed the Iranian mission that the travel authorization will be granted if Iran releases an American citizen," he said.

The United States and Iran are at odds over several issues, including Washington's withdrawal from Iran's 2015 nuclear deal, US accusations that Tehran attacked two Saudi oil facilities on September 14, a charge Iran denies, and Iran's detention of US citizens based on what Washington considers to be false charges. .