“These death sentences and executions are a flagrant breach of international law,” Maya Foa, director of the international human rights organization Reprieve, said Tuesday. “Trials in Egypt routinely fail to meet basic fair trial standards, and this is especially so in mass trials and military tribunals, as in this case.”

Reprieve said the number of people executed in Egypt on Tuesday was the most on a single day since the founding of the modern Egyptian state in 1953.

The families and lawyers of those hanged on Tuesday could not be reached immediately for comment. But Mr. Ghoniem, who is in touch with them, said that the lawyers were not given time to present an appeal after the defense minister signed off on their executions a week ago.

“They are meant to give you 15 days after the signing,” Mr. Ghoniem said. “They got six. How is that fair?”

Islamist activists who know the families said that two of the 15 had bruises and cuts on their bodies, suggesting they had been tortured, and that none of the families were given the chance to say goodbye to the condemned before the executions, as required by Egyptian law.

The Egyptian military did not respond to requests for comment.

Despite the military’s scorched-earth approach to militants in Sinai — including summary executions and the destruction of whole villages — the insurgency there has grown since 2013. A militia that pledged allegiance to the Islamic State in 2014 has since become one of its most effective local affiliates.

The group shot down a Russian jetliner in 2015, killing 224 people. It was also believed to be responsible for an attack on a Sufi mosque in North Sinai last month, killing 311 people in Egypt’s worst terrorist attack. No one has claimed responsibility for the mosque attack, but the Islamic State had publicly identified the town where it took place as a target, and the attackers carried Islamic State flags.