CAIRO — Egyptian prosecutors on Tuesday ordered three detained journalists from the news channel Al Jazeera English to be held in custody for 15 more days, on charges that include belonging to a terrorist group and harming the country's reputation abroad.

Human rights organizations have denounced the charges, accusing the authorities of deliberately confusing the act of reporting on the Muslim Brotherhood with belonging to the group, which has been officially classified as a terrorist organization. Rights advocates said the accusations had sent a worrying signal about the military-backed government's approach to press freedoms.

Four journalists from Al Jazeera were arrested on Sunday, and one, an Egyptian cameraman, was later released. Prosecutors began interrogating the three remaining in custody, including the bureau chief, Mohamed Fahmy, a Canadian-Egyptian citizen; Peter Greste, an Australian correspondent; and Baher Mohamed, an Egyptian producer.

The arrests were part of a widening government crackdown on the Brotherhood, the Islamist group that fell from power after the military's ouster of President Mohamed Morsi, a Brotherhood leader, in July.

Last Wednesday, the government designated the Brotherhood a terrorist group, and in recent days, Egyptian courts have convicted hundreds of Mr. Morsi's supporters who participated in protests, sentencing them to prison.

The charges against the journalists also appeared intended as retaliation against Al Jazeera, the Qatari channel whose Arabic-language service has strongly backed Mr. Morsi and the Brotherhood. The English language news service takes a far more independent editorial position.

Several journalists from both the English- and Arabic-language services have been detained since Mr. Morsi's ouster, and two Al Jazeera Arabic journalists have remained in prison for months.

Prosecutors released a lengthy list of accusations on Tuesday, saying the journalists worked for a network affiliated with the Brotherhood, joined a terrorist group and possessed the kind of equipment typically found in Egyptian news bureaus, including cameras, gas masks and microphones, without a permit.

Mr. Fahmy, a veteran journalist who has worked for CNN and contributed to The New York Times, was singled out in the statement, accused both of terrorism and of turning suites in the Marriott into a news media center where he "manipulated" footage to harm Egypt's reputation, prosecutors said.

A brother, Sherif Fahmy, said that Canadian diplomats had not attended the beginning of his brother's interrogation. Mr. Fahmy, who suffered a dislocated shoulder unrelated to his arrest, had not been allowed to see doctors at Tora Prison, where he was being held, the brother said.

Ragia Omran, a human rights advocate, called the terrorism-related accusations "ridiculous" and said they could be applied to "anyone who works in journalism."

The charges, she said, were part of a pattern of aggressive prosecutions under the military-backed rulers, including convictions of protesters, that were seldom pursued even under Hosni Mubarak, Egypt's authoritarian president who was deposed in 2011.