CAIRO — The world’s most influential Islamist movement is in danger of collapse in the land of its birth — its leaders imprisoned, its supporters slain and its activists branded as terrorists in what many are describing as the worst crisis to confront Egypt’s 85-year-old Muslim Brotherhood.

In the week since Egypt’s new military-backed rulers ordered a brutal crackdown on camps filled with protesters calling for the reinstatement of ousted president Mohamed Morsi, the group that used its organizational muscle to win the country’s first democratic elections, held in late 2011 and early 2012, has been cast into disarray.

Analysts worry that its members, bitter and angry after the deaths of more than 1,000 Morsi supporters in the past week, could abandon the Brotherhood’s decades-long commitment to nonviolence, particularly as its leadership loses its grip on them. Some pro-Morsi demonstrators have been spotted with weapons, and attacks against security forces in the volatile Sinai Peninsula have intensified since Morsi was deposed July 3.

Meanwhile, the movement is battling a level of popular hostility perhaps unprecedented in its history. The Brotherhood’s strategy of confronting the government with sit-ins and marches in recent weeks seems only to have inflamed public opinion.

On Tuesday, Brotherhood supporters vowed that they would not resort to violence as they continued to challenge the interim government installed by the military after Morsi, the group’s standard-bearer, was toppled.

“Our only option is the peaceful method,” Khaled Hanafi, secretary general of the Brotherhood’s Freedom and Justice Party, said at a news conference in Cairo on Tuesday. The detention overnight of the Brotherhood’s “supreme guide,” Mohammed Badie, would not change the group’s approach, he said.

“We regret the arrest of Dr. Badie, but we have chosen a path, and regardless of the sacrifices, we must continue,” Hanafi said.

Badie was interrogated and remanded into pretrial detention Tuesday on a variety of charges, including inciting the killing of protesters outside the Brotherhood’s Cairo headquarters in June. He is also accused of possessing arms, running an illegal gang and assaulting the military. He is scheduled to go on trial with two other Brotherhood leaders this month.

The detention of the Islamist movement’s spiritual leader, whose image was broadcast repeatedly on television after his overnight arrest, seemed to complete the humiliation of the Brotherhood’s leadership. The mass arrests and deaths of its officials have left the group splintered and unable to take coordinated action, analysts say.

An existential crisis

An organization that just two months ago was governing the Arab world’s most populous nation is at risk of falling apart, said Diaa Rashwan, an expert on Islamist movements at Cairo’s al-Ahram Center for Political and Strategic Studies.

“They are facing a really critical moment. They could disappear. And alternatives already exist,” Rashwan said.

The Brotherhood is more than a political or religious group. It has been almost a shadow state in modern Egypt, winning over supporters over the decades with a vast network of charitable services, including dental clinics and thrift shops. It is the “mother of all Islamist movements,” in the words of Shadi Hamid, a Middle East expert at the Brookings Doha Center, having spawned dozens of related groups worldwide since its founding in 1928.