Story highlights Amir Hekmati cites "force, threats, miserable prison conditions"

He says Tehran wants to exchange him for other prisoners

He is a decorated Marine who served from 2001 to 2005

A 29-year-old former U.S. Marine who has been jailed in Iran since 2011 and accused of being a CIA spy says in a letter to U.S. Secretary of State John Kerry that his confession was made under duress.

"For over 2 years I have been held on false charges based solely on confessions obtained by force, threats, miserable prison conditions, and prolonged periods of solitary confinement," Amir Hekmati says in the letter, which was obtained and published by the Guardian and whose authenticity the family vouched for to CNN. "This is part of a propaganda and hostage taking effort by Iranian intelligence to secure the release of Iranians abroad being held on security-related charges."

Hekmati adds that Iranian intelligence told his court-appointed lawyer that he could be released in exchange for two Iranians being held abroad.

The letter Amir Mirza Hekmati wrote to Secretary Kerry.

"I had nothing to do with their arrest, committed no crime, and see no reason why the U.S. Government should entertain such a ridiculous proposition," writes Hekmati, who has dual U.S.-Iranian citizenship. "I do not wish to set a precedent for others that may be unlawfully (obtained) for political gain in the future. While my family and I have suffered greatly I will accept nothing but my unconditional release."

Though Hekmati has been able to send and receive letters, it was not clear how this letter -- dated September 1 -- was sent. The newspaper reported Wednesday that the letter had been smuggled out.

Born in Arizona and raised in Nebraska before settling with his family in Flint, Michigan, Hekmati joined the Marines in 2001 out of high school. He finished his service four years later as a decorated combat veteran with tours in Iraq.

Afterward, he translated Arabic as a contractor and helped train troops in cultural sensitivity.

Hekmati's family said he had gone to Iran to visit his grandmother but was arrested in August 2011, accused by Iran's Intelligence Ministry of working as a CIA agent.

In December 2011, Hekmati appeared on Iranian state television maintaining that he had been sent to Iran by the CIA.

At trial, whose proceedings were not public, prosecutors accused him of trying to infiltrate Iran's intelligence system in order to accuse Iran of involvement in terrorist activities, according to the semi-official Fars news agency.

In January 2012, he was convicted and sentenced to death. Two months later, an Iranian court dismissed the lower court's death sentence and ordered a retrial.

In Washington, spokeswoman Jennifer Psaki said the State Department had received a copy of the letter from Hekmati's family.

But, she added, "We have not had any communication with Iran on the issue of a prisoner exchange."

In a statement issued last month, Kerry said the espionage charges were false and urged the Tehran government to release him "safely and as soon as possible."

Hekmati's mother has visited her son in Tehran's Evin Prison; she says his father has terminal cancer.

Diplomatic relations between Washington and Tehran have been broken since 1980, during the hostage crisis that followed the 1979 Islamic revolution.