Deputy Foreign Minister Abbas Araqchi said the US has taken humanitarian issues "hostage" for political purposes.
American authorities banned Zarif, who is in New York for the annual UN gathering of world leaders, from visiting a city hospital to see Iran's UN Ambassador Majid Takht Ravanchi.
Iran’s UN Mission spokesman Alireza Miryousefi said Takht Ravanchi is being treated for cancer in a hospital not far away in Manhattan’s Upper East Side neighborhood.
In July, the United States imposed tight travel restrictions on Iran’s top diplomat before a visit that month to the United Nations, as well as on other diplomats and their families living in New York, which Zarif described as “basically inhuman.”
Unless they receive prior approval from Washington, they are only allowed to travel within a small area of Manhattan, Queens and to and from the John F. Kennedy airport.
The US State Department confirmed Friday that Zarif wanted to visit “a colleague who is in the hospital receiving world class care.”
The State Department said it would allow the hospital travel request only if Iran released one of several US citizens it is currently "wrongfully detained."
“We have relayed to the Iranian mission that the travel request will be granted if Iran releases a US citizen,” the State Department spokesperson said.
Brian Hook, the State Department’s special representative for Iran, on Monday said if Iran wanted to show good faith, it should release the US citizens it has detained, including Xiyue Wang, a US citizen and Princeton University graduate student who was detained in Iran in 2016.
At a news conference in New York on Thursday, Iranian President Hassan Rouhani said Tehran was open to talking about prisoner swaps, but that the ball was in Washington’s court after Iran’s release of a Lebanese man with US permanent residency in June.
Asked about Americans held in Iran and Iranians imprisoned in the US, he noted that the Trump administration had said that if at least one American was freed by Iran, then Washington would reciprocate.
Rouhani cited the June release of Nizar Zakka, a Lebanese national and permanent US resident detained in 2015 and sentenced to 10 years in prison on accusations of spying for the United States.
“They only thanked Iran,” Rouhani said. “The ball sits in America’s court.”
The United States deported an Iranian woman detained on charges of exporting restricted US technology to Iran on Tuesday.
A judge in Minneapolis sentenced Negar Ghodskani to 27 months in prison on Tuesday, but determined the time she had already spent in custody in Australia and the United States was enough to fulfill her punishment.
A legal resident of Australia, Ghodskani was arrested in Adelaide in 2017 after US prosecutors said she sought US digital communications technology by presenting herself as an employee of a Malaysian company.
Pregnant at the time of her arrest, she gave birth while in Australian custody. Her son was sent to Iran to live with his father.
During a visit to New York in April, Zarif raised her case, floating a potential prisoner swap for a British-Iranian woman, Nazanin Zaghari-Ratcliffe, being held in Tehran for sedition.
US Secretary of State Mike Pompeo on Thursday declined to discuss the possibility of a US-Iranian prisoner swap after Ghodskani’s deportation.
Reuters, AP and AFP contributed to this story.