A State Department official said in an emailed statement that it was aware of Mr. Zarif’s comments and that the United States had repeatedly called for a “humanitarian resolution” of prisoner cases.
“The Iranian regime can demonstrate its seriousness regarding consular issues, including Iranians who have been indicted or convicted of criminal violations of U.S. sanctions laws, by releasing innocent U.S. persons immediately,” the official said.
It is unclear whether American officials would be open to a prisoner exchange with Iran.
Mr. Zarif spoke as the Trump administration has been intensifying American sanctions on Iran. On Monday the administration took steps aimed at stopping Iran’s five biggest customers from buying Iranian oil, the country’s most vital export.
The Americans held in Iran include at least two dual citizens: Siamak Namazi, a business consultant, and his father, Baquer Namazi, a former Unicef diplomat. The two other Americans known to be held are Xiyue Wang, a Princeton graduate student, and Michael R. White, a Navy veteran. Robert A. Levinson, a former F.B.I. agent, has been missing in Iran since 2007, and family members have said they believe he is alive.
A lawyer for the Namazis did not immediately respond to a request for comment on Mr. Zarif’s exchange proposal. Hua Qu, Mr. Wang’s wife, said in an email, “My husband did nothing wrong or illegal and I would encourage all governments to come together so he can be released and come home to us.”
Jonathan Franks, a spokesman for Mr. White’s family, said in an email he did not have enough information to comment on Mr. Zarif’s proposal, but that “we’re in favor of the United States taking any reasonable step that might bring about Michael’s release.”
Mr. Levinson’s relatives, who have long rejected Iranian government claims of ignorance regarding his whereabouts, had a mixed response to Mr. Zarif’s proposal.
“We strongly desire to see any action that will bring our father home to us after 12 years of captivity,” the family said in a statement. “What’s phony is the idea that Iranian authorities don’t know where our father is. Let’s finally resolve this.”