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But there is one major Islamist faction among their ranks — the ultraconservative al-Nour Party, which broke with Mr. Morsi months ago.

Mr. ElBaradei is considered one of the inspirations of the revolutionary groups that led the 2011 uprising against autocrat Hosni Mubarak, but many Islamists distrust him, seeing him as too secular.

Liberal and secular factions were infuriated by al-Nour’s rejection of Mr. ElBaradei. The youth activist group Tamarod accused it of “blackmail” and “arm-twisting.” But at the same time, they are eager to keep al-Nour on their side to show that Mr. Morsi’s removal had support among at least some in the Islamist movement.

A senior official in the National Salvation Front, in which Mr. ElBaradei is a leader and Mr. Bahaa-Eldin is a member, said Mr. ElBaradei would accept the compromise if Mr. Bahaa-Eldin does as well, with the two seen as partners in a leadership team. During the transition, the prime minister will hold most governing powers, with the president a largely ceremonial post. A top judge, Adly Mansour, was sworn in last week as interim president.

The prime minister also likely will have strong influence on the process of writing a new constitution. That’s a major concern of al-Nour, which pushed hard for the Islamic character of the charter pushed through under Mr. Morsi’s administration, which was suspended after his ouster.

Walid el-Masry of Tamarod said al-Nour is using the ElBaradei issue to press liberals on the constitution, worried about changes to the Islamist-drafted charter.

“They are afraid about the articles that concern the state’s Islamic identity,” he said, adding that the liberals have assured Salafis that they won’t touch these articles.

The Islamists have denounced the removal of Mr. Morsi as an army coup against democracy. Their opponents have argued the president squandered his electoral mandate and that the Brotherhood was putting Egypt on an undemocratic path.

Pro-Morsi rallies turned out in several places around the city Sunday, centered outside the Rabaah al-Adawiya Mosque, where they have been holding a sit-in for more than a week.

In a Facebook posting Sunday, the Brotherhood’s supreme leader, Mohammed Badie, said the “leaders of the unconstitutional coup continue flagrant violations against the Egyptian people.”

Senior Brotherhood member Saad Emara said there was no possibility for any negotiations with the new leadership after “all betrayed us” and after the military’s clampdown on the group.

“We are not regressing to a Mubarak era but to … a totalitarian regime,” he told The Associated Press. “Anything other than protest is suicide.”

Mr. Morsi and five top Brotherhood figures are in detention, and about 200 others have arrest warrants out against them. The group’s TV station and three other pro-Morsi Islamist stations were put off the air. Among those detained is Mr. Badie’s deputy, Khairat el-Shater, seen as the most powerful figure in the group and its main decision-maker.

A Brotherhood spokesman, Gehad el-Haddad, said the military is not giving any positive signals for the group to be willing to talk, pointing to the arrests of the leadership figures and shutdowns of media.

“They are trying to terrorize us,” he said.

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