The family of a former US Marine held for 555 days in Iran, mostly in solitary confinement, urged Iranian leaders on Tuesday to show mercy and free him, revealing his father is dying from cancer.

Amir Mirzai Hekmati, 29, who is a US citizen born in America to parents of Iranian origin, was detained in August 2011 while visiting his elderly grandmother on his first trip to Iran.

He was accused of being a CIA operative, charges which have been vigorously denied by his family and by the US State Department.

The family has now written to Iranian supreme leader Ayatollah Ali Khamenei, calling for mercy to mark the Persian New Year which falls on March 20.

"We want to emphasize that our family's not political. We're American citizens. Amir's an American. We are not trying to involve ourselves in the politics between Iran and the US," brother-in-law Ramy Kurdi told AFP.

Iranian authorities have in the past released prisoners as a goodwill gesture to mark the New Year, and Kurdi said it was the family's "hope and prayer" that Hekmati would be among them.

His father, Ali, a microbiology professor in his early 60s, had an operation to remove a brain tumor several months ago and has undergone chemotherapy.

"He's very strong, he's very passionate about seeing his son again so we're making great efforts to do that," Kurdi said, adding Hekmati did not know his father was ill.

A year ago a death sentence, imposed on Hekmati after a closed-door trial, was overturned by the Iranian Supreme Court, and his case was sent for retrial. But there have been no new legal moves.

Hekmati, who is from Michigan, has only been allowed brief visits from relatives. His mother has seen him twice in prison, but on her third trip in June she was turned away.

Another relative, who was then allowed to visit in February, revealed Hekmati had gone on a month-long hunger strike late last year to protest months of solitary confinement in the notorious Evin jail.

He was finally moved out of solitary and given medical treatment when he passed out. But his family is concerned about his health.

"Although a year ago today the Supreme Court lifted the death sentence and ordered a retrial, Mr. Hekmati's case remains in limbo and his status is uncertain," State Department acting deputy spokesman Patrick Ventrell told AFP.

Ventrell said the charges against Hekmati were "categorically false" and said Washington was concerned for his health, urging Iranian authorities to allow a visit from Swiss embassy officials who represent the US in Tehran.

The US also "urges the Iranian government to release him so that he may be reunited with his family," Ventrell added.

Kurdi added: "We just want Amir home. His father is ill and his time on Earth is limited, and he wants to enjoy that time with his son, and we think he has that right."