“Wherever an Iranian is, as the Islamic Republic of Iran’s government, we feel that it is our duty to defend their rights,” he said.

Still, most Iranian officials did not talk about the prisoner deal. Even Mr. Rouhani conspicuously omitted any reference to it in a news conference on Sunday.

Political analysts in Iran said the silence reflected the delicacy of engaging in cooperative arrangements with the United States, which risks the perception of weakness in the face of a hostile power.

“In Iran, negotiations with the enemy are done in secrecy,” said Nader Karimi Joni, an Iranian journalist. “Even years later, officials only reveal details when it is in their interest or when they are forced to react to revelations by the other party.”

Iran’s silence also added to the unknowns surrounding the fourth freed Iranian-American, whose name was given by the State Department as Nosratollah Khosravi-Roodsari.

It seemed that nobody in Iran knew he had been arrested, and nobody seemed to know any more about him. When the Swiss diplomats who had arranged for the departure of the other three Americans offered him a seat on their plane, they said, Mr. Khosravi-Roodsari opted to stay.

It was not made clear how this offer had been communicated.

In the hours after the news of the prison exchange broke of Saturday, the semiofficial Fars news agency, one of the few Iranian outlets reporting it, did not mention Mr. Khosravi-Roodsari’s name. Instead it reported that the fourth Iranian-American was Siamak Namazi, a business consultant arrested in October.