Increasingly desperate to return to the United States, a Marine veteran of Iranian descent who has been incarcerated in Iran for three and a half years has renounced his Iranian citizenship, requested deportation and accused Iran of using American prisoners as “bargaining chips,” his family said Monday.

“Once deported, he promises never to return,” the family of the Marine veteran, Amir Hekmati, a dual citizen of the United States and Iran, said in a statement.

The statement also detailed what it described as a litany of previously undisclosed torture and other abuses — including feet whippings, Taser hits to the kidneys, sleep deprivation and extended solitary confinement — suffered by Mr. Hekmati in the Iranian penal system since he was arrested in August 2011.

There was no immediate comment from the judicial authorities in Iran or from Mr. Hekmati’s Iranian lawyer, Mahmoud Alizadeh Tabatabaei, about Mr. Hekmati’s renunciation of citizenship or new assertions of mistreatment. Mr. Tabatabaei has said before that he would try different approaches to secure his client’s freedom.

The family released a copy of a letter it said Mr. Hekmati had written, addressed to the Iranian interests section of the Pakistan Embassy in Washington, where he acquired his Iranian passport so he could visit relatives in 2011.

Mr. Hekmati stated in the letter that it had “become very clear to me that those responsible view Iranian-Americans not as citizens or even human beings, but as bargaining chips and tools for propaganda.”

For that reason, the letter stated, “I formally renounce my Iranian citizenship and passport.”

Mr. Hekmati, 31, who was born in Flagstaff, Ariz., grew up in Flint, Mich., and served with the Marines in Iraq, is one of at least three American citizens of Iranian descent known to be imprisoned in Iran.

The Iranian authorities do not recognize dual citizenship. They regard all three as Iranian citizens, regardless of birthplace, and have treated them accordingly, denying them the consular access that is afforded to foreign inmates.

Their cases have acquired added significance as Iran and the United States have intensified efforts to reach an agreement on Iran’s disputed nuclear program. The deal, if completed, could potentially lead to a broader thaw in the longstanding estrangement between the two countries.

It was not clear from the family’s statement why Mr. Hekmati believed that renouncing his Iranian citizenship might be a means of leaving the country. Iranian human rights advocates said they had not seen this strategy used before.

“It’s creative,” said Hadi Ghaemi, the executive director of the International Campaign for Human Rights in Iran, a group based in New York. “I’m not sure that it will work.”

Mr. Hekmati was convicted of espionage after what the family has described as a forced confession. He was sentenced to death, but the verdict was reversed and he was convicted of the lesser charge of aiding a hostile country, meaning the United States, and sentenced to 10 years.

He and his family have repeatedly asserted that he is innocent and have implored the Iranian authorities to release him, if for no other reason than so he could return to Flint and see his father, Ali, who has terminal brain cancer.

Obama administration officials say they have raised his case — and those of the other prisoners — numerous times on the sidelines of the nuclear talks.

The new accusations that Mr. Hekmati has been tortured in prison were based on what the family’s statement described as accounts from “his family in Michigan, his extended family in Iran and from Amir himself.”

They said he had been held in solitary confinement for the first 17 months, often in stress positions for extended periods, and had not been allowed to speak with his family by phone for 20 months. “Cold, foul-smelling water was repeatedly poured into his cell to prevent him from sleeping,” the statement said.

He was also forcibly given drugs including lithium, Tasered in the kidneys during interrogations, whipped on the feet with cables and subjected to “mental torture through threats, insults and humiliations,” the statement said.

It repeated a complaint Mr. Hekmati made last December about the conditions of his imprisonment, asserting that he had been housed with hardened criminals and drug dealers and that “he experiences recurring lung infections, his cellmates have lice, and he is surviving on a diet of only rice and lentils.”

The release of the statement coincided with a new report by the United Nations human rights investigator for Iran, Ahmed Shaheed, asserting that political repression and use of the death penalty in Iran are rising.

The other Americans incarcerated in Iran are Jason Rezaian, 39, of Marin, Calif., The Washington Post’s Tehran correspondent, who has been held on unspecified charges since July; and Saeed Abedini, 34, of Boise, Idaho, a pastor sentenced in 2013 to eight years in prison on charges of disturbing national security through a private network of churches.

A fourth American, Robert A. Levinson, disappeared while visiting Iran in 2007. Iranian officials say they have no information on his whereabouts. Last Tuesday, on the eighth anniversary of Mr. Levinson’s disappearance, the United States quintupled, to $5 million, its reward for information that could lead to his safe return.