Relatives of a former Marine imprisoned in Iran for more than three years said Tuesday that he had begun a hunger strike, and they released an open letter he had written to President Obama urging him “not to forget me” as the United States intensifies negotiations with the Iranians on their disputed nuclear program.

Those negotiations, which have already been extended twice and are now facing a July deadline, resumed on Tuesday in Geneva between Iran and the group of six big powers, including the United States, that have been seeking guarantees of Iran’s peaceful intentions for its nuclear program.

The letter by the former Marine, Amir Hekmati, 31, of Flint, Mich., was his first to Mr. Obama, and reflected despondency over the paralysis of his case.

“I have dictated this letter to my family and asked them to bring my plight to your attention through an open letter,” it reads. “It is my hope that after reading this letter you, or anyone who may see this, will help end the nightmare I have been living.”