"With the utmost respect, Mr. President, I fear that my government - the very government I was serving when I began this nightmare - has abandoned me. Officials in your administration have expressed sympathy and called for my unconditional release, and I very much appreciate that. But it has not brought me home," he wrote.
Gross is not the only one urging Obama to get involved. In late November, 66 senators led by Sen. Patrick Leahy, a Democrat, sent Obama a letter asking him to "act expeditiously to take whatever steps are in the national interest" to obtain Gross' release.
White House press secretary Jay Carney on Tuesday called upon the Cuban government to release Gross and said that Obama has "personally engaged foreign leaders and other international figures to use their influence with Cuba to promote" his release.
Gross' wife, Judy Gross, who now lives in Washington, also held a rally Tuesday in front of the White House. She urged the president to "do whatever it takes to bring Alan home."
"Please, Mr. President, don't leave Alan to die in Cuba," she said, addressing a crowd holding posters reading "Bring Alan Home."
Cuba has previously expressed a willingness to release Gross if the United States makes a similar gesture involving the so-called Cuban Five, intelligence agents who were sentenced to long jail terms in the United States in 2001. One of the men was released from prison in 2011 and was allowed to return to Cuba this year. A second is scheduled for release in February.
In a statement broadcast on Cuban state TV on Tuesday night, Josefina Vidal, the Foreign Ministry's top diplomat for U.S. affairs, said the Cuban government "reiterates its willingness to immediately establish a dialogue with the U.S. government to find a solution to the case of Mr. Gross on reciprocal bases that take into account Cuba's concerns linked to the case of four Cuban antiterrorist fighters imprisoned in the United States."
The United States has in the past rejected a trade, and the State Department in a statement Monday called on Cuba to release Gross "immediately and unconditionally." But Judy Gross said Tuesday that she believes the U.S. government should negotiate to bring her husband home. She said she does not know what the Cuban government wants in exchange.
Over the past year, U.S and Cuban officials have made some progress on repairing their relationship. U.S. and Cuban representatives met twice this year for renewed talks on re-establishing direct mail service, 50 years after it was stopped amid Cold War tensions. The two countries also resumed talks this year about migration issues. Both sets of talks had been on hold since Gross' arrest.
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Follow Jessica Gresko at http://twitter.com/jessicagresko