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Interim Vice President Mohamed ElBaradei, a Nobel Peace Prize laureate, reportedly favors talks with the Muslim Brotherhood to end the crisis.

Mr. Morsi was ousted by the military July 3 after four days of protests with millions of Egyptians taking to the streets against his administration. The protesters accused Mr. Morsi of monopolizing power and looking out only for the interests of the Muslim Brotherhood.

Since Mr. Morsi’s ouster, at least 140 people, a majority the former president’s supporters, have been killed in clashes with security forces.

Despite the bloodshed, the protesters have no intention of packing up.

“The sit-ins will continue until [Mr. Morsi] is restored [as president] and constitutional legitimacy is restored. Only then can we talk about what to do next,” Muslim Brotherhood spokesman Gehad El-Haddad said.

Time for soccer

Tens of thousands of protesters, including women and children, have transformed the two Cairo squares into tent cities, where life carries on as close to normal as possible. Earlier this week, protesters from the two sites squared off in a soccer game.

“The danger [for the Muslim Brotherhood] is that [calling off the sit-ins] will be an admission of defeat,” Mr. Sabry said. “Staying in the streets is the biggest card [the Muslim Brotherhood has] to ensure they don’t end up being persecuted and have a strong hand in any negotiations.”

Mr. Morsi has been detained at a secret location since his ouster. On Monday, an Egyptian judge extended his detention by 15 days. He has been accused of conspiring with the Palestinian terrorist group Hamas to break out of prison two days after his arrest in 2011 during the uprising that toppled his predecessor, Hosni Mubarak.

Other senior Islamist leaders have been arrested or face arrest warrants on charges of inciting violence.

Credibility at stake

The Muslim Brotherhood also risks losing face among its supporters if it backs down.

“If, having stood on the argument for law and order … they say, ‘The coup is legitimate. We were wrong. We’re going home’ — then not only they will they be under the threat of arrest and liquidation, they would have also lost all their ideological legitimacy,” said Jonathan Brown, an associate professor of Islam and Muslim-Christian understanding at Georgetown University.

“Having exposed so much of their network, their activities and their capabilities to the light of day, they are now even more vulnerable than they were before the protests that ousted Mubarak. So they really are going to be in a position of potentially complete elimination,” he added at a forum hosted by the Middle East Institute in Washington last week.

The Muslim Brotherhood was banned in Egypt 1954, but it emerged on the national stage after Mr. Mubarak was ousted on Feb. 11, 2011, following pro-democracy protests. After initially saying it would not participate in the presidential elections, the Muslim Brotherhood went on to field Mr. Morsi as its candidate for president last year.

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