Each side, in effect, has prisoners to use as a bargaining chip.
The Iranians say at least 14 Iranians have been unfairly imprisoned or prosecuted by the United States or its allies, mostly on what they call specious accusations of sanctions violations. The list includes a friend of Foreign Minister Mohammad Javad Zarif, and a pregnant woman held in Australia who could be extradited to the United States.
Last week, in what has been widely seen as a way of telegraphing a possible prisoner exchange, Iranian state television broadcast reports on two Western prisoners held in Iran: Nazanin Zaghari-Ratcliffe, 38, a Briton of Iranian descent employed by the Thomson Reuters Foundation, who was sentenced to five years, and Xiyue Wang, 37, an American of Chinese descent working on his Ph.D. in history at Princeton University, who was sentenced to 10 years.
On Tuesday, a State Department spokeswoman, Heather Nauert, condemned the videos and reiterated the American demand for Iran to release all prisoners who are “unjustly detained, in particular American citizens.” She did not answer when asked about the possibility of a dialogue with Iran on the prisoner issue.
Hua Qu, Mr. Wang’s wife, said in a telephone interview that she thought the television broadcast was “a step forward,” although she implored the Trump administration to do more to help free her husband and other incarcerated Americans.
“They have promised many times it’s their first priority, to bring back our hostages,” Mr. Wang’s wife said. “My husband has been behind bars for 16 months; he has arthritis in both knees, back pain, headaches.”
Earlier, in an interview with NBC News, she said her husband was “extremely stressed, he has depression and he attempted to commit suicide.”
At least four American citizens and two permanent residents of the United States are known to be held in Iranian prisons. A fifth American, Robert A. Levinson, has been missing in Iran for more than a decade.
Besides Mr. Wang, speculation about a possible exchange also has centered on Baquer and Siamak Namazi, a father and son who are each serving 10-year terms.
Considerable diplomatic pressure has been exerted on Iran concerning the older Mr. Namazi, a former Unicef diplomat who is about to turn 82 and suffers from a number of maladies, including heart disease.
Jared Genser, a lawyer in Washington for the Namazi family, said Tuesday that their conditions of confinement had improved compared with a year ago. That being said, he added, the Iranian government had recently “taken a tougher line,” possibly in connection with the Trump administration’s hostility.
“Baquer has lost six teeth from malnutrition,” Mr. Genser said, adding that while his client had been fitted for implants, the Islamic Revolutionary Guards Corps, which controls the wing of Evin Prison where he is confined, “have refused to allow the implants.”
Still, Mr. Genser said, the prison authorities have permitted cardiologists to install a pacemaker in the father — a possibly telling indicator of his worth to them as a bargaining chip.
“I hope the government of Iran appreciates that the value that Baquer Namazi might serve is dependent on his being alive — particularly if there was a prisoner swap,” Mr. Genser said. “If he were to die, the consequences would be severe, and no government in the world would defend Iran.”
Mr. Wang was arrested last year while researching public records in Iran for his doctoral thesis on an Iranian dynasty that ended last century. He was accused of passing documents to the State Department.
Iranian state television’s broadcast about Mr. Wang, on Sunday, showed him wearing a white prisoner uniform while under interrogation. He explains that he visited several archives. “That’s it,” he is heard saying.
The authorities have alleged that he illicitly scanned 4,500 pages of digital documents, paid thousands of dollars to access archives he needed and sought access to confidential areas of Tehran’s libraries.
Princeton repeatedly has asserted his innocence and said that he had received government permission for his research. In an emailed statement on Monday, Daniel Day, a Princeton spokesman, said the Iranian broadcast had been “filled with false and misleading statements about Mr. Wang and about Princeton.”
The television broadcast on Mrs. Zaghari-Ratcliffe, last Thursday, included close-ups of an April 2010 pay stub from her previous employer, the BBC World Service Trust. Iran is suspicious of the BBC because it broadcasts a Persian-language satellite television channel that competes with state television.
The Iranian broadcast included a June 2010 email, found in her inbox by interrogators from the Revolutionary Guards, in which she wrote about the “ZigZag Academy,” a BBC World Service Trust project, which trained “young aspiring journalists from Iran and Afghanistan through a secure online platform.”
Both her husband, Richard Ratcliffe, and Thomson Reuters repeatedly have emphasized that she was not training journalists or involved in any work regarding Iran while there. But their assertions were undermined a few weeks ago when Boris Johnson, Britain’s foreign secretary, told Parliament in an apparent gaffe that Mrs. Zaghari-Ratcliffe had been “teaching people journalism.”
Mr. Johnson, who is scheduled to travel to Iran in the coming month, retracted the remark, but Iranian state television described it as proof of her “crimes.”
Mr. Ratcliffe has said his wife is now worried that because of Mr. Johnson’s remarks, her five-year sentence could be increased to 10 years. She has a second trial scheduled on Dec. 10.
Iranian and British officials in the past months have hinted there could be a compensation of about $500 million for a decades-old dispute over roughly 1,500 British Chieftain tanks, paid for by Iran but never delivered after the 1979 revolution.
Officials from both countries insist Mrs. Zaghari-Ratcliffe’s case is not related to the debt repayment. But on Tuesday, Iran’s Judiciary spokesman, Gholamhossein Mohseni Ejei, seemed to draw a connection.
Mrs. Zaghari-Ratcliffe, who has been held in Iran since April 2016, could be granted “conditional release” if she qualifies for it, he was quoted as saying by ISNA, the semiofficial student news agency.
Asked whether Britain’s payment of its debt to Iran could play a part in the case, Mr. Ejei was quoted as saying that any country would try to secure the release of its citizens imprisoned in another country and that “we would do the same if we have any imprisoned abroad.”