He and the others in the case were reportedly accused of joining a command center at the sit-in that sought to spread chaos across Egypt in defiance of the government.

Mr. Soltan has conducted a hunger strike for more than a year to protest his imprisonment, according to his family. In a recent letter to the family that was provided to The New York Times, American diplomats working on the case warned that his hunger strike “has done and continues to do severe, in some cases irreparable, damage to his body” and “is a significant threat to his life.”

In a letter smuggled from prison and published on the website of The Times in early 2014, Mr. Soltan recalled volunteering for Mr. Obama’s presidential campaign and appealed to the president for help. “I often get asked sarcastically by judges, officers, and even inmates, ‘Where is this first world country that takes such pride in defending human rights and freedoms? Where are they now to help you?’ ” Mr. Soltan wrote. “Of course, I am left speechless every time.”

In another smuggled letter, published on the website in November 2014, Mr. Soltan compared prison to his struggles as a junior varsity basketball player. “Just like I was prepped to be a better basketball player, I was being molded by God to be a wiser human, an effective leader, and a stronger advocate of freedom and peace,” he said.

In a telephone interview from the Washington area on Friday, his sister, Hanaa Soltan, said her family had been stunned by the death sentence for her father when it was first reported a few weeks ago.

“No one was really expecting it,” she said, adding, “I knew that when the sentencing came on, my dad was going to get a really tough one but — death sentence — I don’t think there’s really ever anything that prepares you for that.”

Egypt’s government has banned the Muslim Brotherhood, Egypt’s mainstream Islamist movement, and labeled it a terrorist group.