Hopes Rise for Appeal of Ex-Marine Held in Iran Prison life has markedly improved in recent weeks for Amir Hekmati, the former Marine incarcerated for nearly two years in Iran on spying accusations. His sister said he was now allowed weekly visits from three Iranian relatives, books, daily exercise and a regular correspondence of letters with family in the United States. His sister, Sarah Hekmati, who shared two of the letters, said Mr. Hekmati was also attending Persian language classes in Evin Prison in Tehran and had started to teach English to fellow inmates. She said that the two uncles and an aunt who had visited him said he was sounding increasingly positive and optimistic. "Even from his letters, he's embraced this as a test, as a way of reshaping him," Ms. Hekmati said Tuesday in a telephone interview. He feels like he's been productive. The improved circumstances, she said, strengthened the family's hope that Iran's judiciary, which threw out his original conviction for espionage but has not yet announced a retrial, would favorably review a legal appeal for his release prepared by Mr. Hekmati's Iranian counsel. "Our relatives on the ground say people are optimistic," Ms. Hekmati said. It was unclear whether the eased prison conditions were related to the presidential elections in Iran last month, in which a moderate cleric, Hassan Rowhani, defeated his more conservative rivals. Mr. Rowhani, who has said he wants to find ways to improve Iran's estranged relations with the United States, is scheduled to take office in early August. There has also been speculation that Mr. Hekmati may be among the inmates in Iran's penal system who are sometimes granted clemency or reduced sentences during Ramadan, the monthlong Muslim holiday that began Wednesday in Iran. So far, however, there has been no word from the Iranian authorities on the disposition of Mr. Hekmati's case, which has become something of an emotional cause in his home state, Michigan, and an additional source of Iranian-American tensions. Mr. Hekmati learned during his incarceration that his father, a college professor in Flint, has brain cancer, which has made his relatives more anxious about when Mr. Hekmati might be freed. Senator Carl Levin, the longtime Michigan Democrat, spoke on the Senate floor on June 12 calling for Mr. Hekmati's release, noting that even Iran's Supreme Court had found the evidence against him deeply flawed and that Iranian officials had yet to make clear what charges, if any, he might face. Mr. Hekmati, who spent four years in the Marines and turns 30 on July 28, was arrested in August 2011, interrupting what his family has described as an innocuous visit with his grandmothers. He disappeared for three months, before the Iranian authorities paraded him in a heavily edited television broadcast as a C.I.A. spy. He was tried and sentenced to be executed, but the verdict was overturned and in March 2012 a new trial was ordered. Mr. Hekmati has remained in Evin Prison throughout, however, with little access to outside counsel. He spent many months in solitary confinement and went on a hunger strike. His family has said conditions began to improve only this past March, when an uncle was allowed to visit for the first time and Mr. Hekmati was permitted to send a few letters home, in which he apologized for having caused his family so much angst. Until a few weeks ago, his sister said, Mr. Hekmati had been receiving visits just once a month from the uncle, their mother's brother. Now, she said, he is receiving visits every Monday, and the visitors included his father's brother and sister. In one of his recent letters to their mother that Ms. Hekmati shared, he sought to reassure the family that he was doing well. "I am living a very healthy life here," he wrote. There are very good people here. In regards to food we have everything we need. I attend language classes and I exercise daily. Please forgive me for being a source of your worries. He also wrote, "I have a good feeling that this situation will be resolved soon, God willing." Mr. Hekmati described his anguish over his father's cancer and beseeched him to "stay strong and do not worry about me at all."