Egypt’s military-backed authorities arrested the Muslim Brotherhood’s supreme leader on Tuesday, dealing a serious blow to the embattled movement at a time when it is struggling to keep up street protests against the ouster of President Mohamed Morsy in the face of a harsh government crackdown.

The Brotherhood’s spiritual guide, Mohammed Badie, was arrested in an apartment in the Cairo district of Nasr City, close to the site of a sit-in encampment that was forcibly cleared by security forces last week, triggering violence that killed hundreds of people.

Mr. Badie’s arrest is the latest move in an escalating crackdown by authorities on the Brotherhood, which has seen hundreds of its members taken into custody.

The Muslim Brotherhood said Mr. Badie’s detention would not weaken the movement or lead its followers away from their principles.

“The people will continue their peaceful struggle until they regain all their rights with his eminence, the guide (leader) in jail,” it said.

The group’s near-daily protests since Mr. Morsy’s ouster have diminished in recent days, with scattered demonstrations in Cairo and elsewhere attracting mere hundreds, or even dozens, of protesters. On Tuesday, several hundred Mr. Morsy supporters staged protests in Helwan, an industrial suburb north of Cairo, and in Ein Shams, a residential district on the opposite end of the city, shortly before the 11-hour curfew went into effect at 7 p.m.

Mr. Morsy has been detained in an undisclosed location since the July 3 coup that ousted him, following protests by millions of Egyptians against his rule. He is facing accusations of conspiring with the militant Palestinian Hamas group to escape from prison during the 2011 uprising and complicity in the killing and torture of protesters outside his Cairo palace in December.

Mr. Badie’s last public appearance was at the Nasr City protest encampment last month, where he delivered a fiery speech from a makeshift stage in which he denounced the military’s removal of Mr. Morsy. His arrest followed the killing of his son Ammar, who was shot dead during violent clashes between security forces and Mr. Morsy supporters in Cairo on Friday.

Mr. Badie and his powerful deputy, Khairat el-Shater, are to stand trial later this month on charges of complicity in the killing in June of eight protesters outside the Brotherhood’s national headquarters in Cairo.

Mr. Badie was taken to Tora prison in a suburb south of Cairo, where a team of prosecutors was questioning him, security officials said, speaking on condition of anonymity because they were not authorized to talk to the media.

Tora is the same sprawling complex where ex-president Hosni Mubarak, ousted in the 2011 popular uprising, is being held, along with his two sons. Several Mubarak-era figures are also imprisoned there, as are several Brotherhood leaders and other Islamists.

After his arrest, the private ONTV network showed footage of a sombre-looking Mr. Badie sitting motionless on a black sofa as a man in civilian clothes and carrying an assault rifle stood nearby.

Meanwhile, the Brotherhood released the text of Mr. Badie’s weekly message to the group’s followers. Quoting heavily from the Quran, he warned that anyone who supports the current “oppression, suppression and bloodshed” including Arab and foreign governments will soon regret their stand.

In the aftermath of last Wednesday’s violent crackdown on the sit-in camps, the military-backed government is considering outlawing the Brotherhood, which has spent most of the 85 years since its creation as an illegal organization. The government has asked the judiciary for advice on how to go about a ban. It has also come under growing pressure from pro-government media and a wide array of secular politicians to declare the Brotherhood a terrorist organization.

Brotherhood spokesman Ahmed Aref sought to downplay the significance of Mr. Badie’s arrest, writing on his Facebook page Tuesday “Mohammed Badie is one member of the Brotherhood.”

Mr. Badie’s arrest came a day after suspected Islamic militants ambushed two minibuses and killed 25 off—duty policemen in Egypt’s Sinai Peninsula.

The daylight attack raised fears that the strategic desert region bordering Israel and the Gaza Strip could be plunged into a full-fledged insurgency.

The Sinai Peninsula has long been wracked by violence by al-Qaeda-linked fighters, some who consider Mr. Morsy’s Brotherhood too moderate, and tribesmen who have used the area for smuggling and other criminal activity. Attacks, especially those targeting security forces, have been on the rise since Morsi’s ouster.

Monday’s attack took place near the border town of Rafah in northern Sinai. A few hours later, militants shot to death a senior police officer as he stood guard outside a bank in el-Arish, another city in the largely lawless area, security officials said. Nobody claimed responsibility for either attack.

Meanwhile, a little-known law professor, Sayed Ateeq, filed a case against Mohamed ElBaradei, accusing the Nobel Peace Prize laureate of committing “high treason” and damaging the country’s world image by quitting his job as interim vice president last week. Egyptian law allows citizens to file cases like that, although many are swiftly thrown out by judges.

Mr. ElBaradei quit to protest the use of force by security forces in clearing the Morsy supporters’ sit-in camps, warning the violence will only breed more violence and play into the hands of extremists. He has since been the target of a media and political campaign accusing him of abandoning the country at a time when his services were most needed. Some questioned his credentials as a politician who could withstand the pressures of politics.

Elsewhere, soldiers killed an Egyptian journalist working for the country’s state-run flagship daily Al-Ahram newspaper at a military checkpoint, security officials said Tuesday. Tamer Abdel-Raouf’s death brings to five the number of journalists who have died in the past week of violence in Egypt.

The military initially said that Abdel-Raouf sped through a checkpoint Monday evening after a nighttime curfew began, and that soldiers fired warning shots before shooting at the car. It said the military did not deliberately shoot to kill.

The two journalists had just finished a meeting with the recently appointed governor of Beheira province, northwest of Cairo.

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