Iran’s foreign minister offered publicly on Wednesday to negotiate a prisoner exchange with the United States, saying he had been authorized to conduct such talks.

It appeared to be the first time that the foreign minister, Mohammad Javad Zarif, had made such a proposal openly, in what seemed like a diplomatic overture in a worsening relationship with the United States under the Trump administration.

“I put this offer on the table publicly now, exchange them, all these people that are in prison inside the United States, on an extradition request from the United States,” Mr. Zarif said during a talk at the Asia Society in New York, where he was attending a meeting at the United Nations.

“We believe their charges are phony. The United States believes charges against these people in Iran are phony,” Mr. Zarif said. “Fine, let’s not discuss that. Let’s have an exchange. I am ready to do it and I have the authority to do it.”