Published by The New York Times on August 13, 2015. Written by Julie Hirschfeld Davis and Peter Baker.

Mr. Gross’s lawyer, Scott D. Gilbert, told the White House that if his client died, Mr. Obama would shoulder the blame. “We’re now at the point where we’re bringing my client out on the plank,” Mr. Gilbert told Mr. Zuniga during a tense meeting at the White House. “If you don’t deliver on this, Alan is going to die, and this whole thing will blow up in your face.”

Mr. Gilbert threatened to sue Mr. Obama on the eve of the 2014 midterm elections for failing to uphold the Hostage Act of 1868, which requires the president to take all action short of war to free an American captive held unjustly by a foreign government.

Mr. Kerry sent a handwritten note of encouragement to Mr. Gross, followed by the president’s letter. Mr. Gilbert delivered them in separate trips to the military hospital in Havana where he was held. He also brought cryptic updates for Mr. Gross on efforts to win his release, typed into the body of routine legal memos to avoid detection.

Restoring Relations

By then, the talks had moved beyond Mr. Gross into details about restoring diplomatic relations and reopening embassies. In September, Mr. Rhodes and Mr. Zuniga arrived at the Vatican to present the entire package to senior advisers to the pope’s advisers.

“At that point, you’re on the hook to the pope,” Mr. Rhodes recalled. “When we walked out of the Vatican, we knew this was over. That was the moment when I kind of exhaled.”

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