The Michigan family of a former Marine incarcerated for more than three years in Iran has been receiving telephone calls and emails from that country proposing prisoner swaps for Iranians held in the United States, he said in a letter to Iran’s president made public by his relatives on Tuesday.

The former Marine, Amir Hekmati, 31, said that he and his family had rejected the idea of such exchanges. He reiterated his contention that he is innocent and should be released.

The letter also disclosed previously unpublicized details of Mr. Hekmati’s confinement in Evin Prison in Tehran — including assertions of isolation in a 3-foot-by-3-foot cell for the first four months, and starvation and deception by Iranian officials — that the family had known but kept private.

“My family endured the most painful and horrific four months of their lives, wondering what became of me,” he wrote in the letter, addressed to President Hassan Rouhani of Iran.