Demonstrators at the Republican Guard barracks, where three people were killed on Friday, shouted "Morsi, Morsi, God is greatest!" and "Peaceful, peaceful!" as soldiers and policemen looked on from behind barbed wire.
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"We will not leave until Morsi returns. Otherwise we'll die as martyrs," said 55-year-old Hanim Ahmad Ali Al-Sawi, wearing a veil over her face in the searing midday sun. "This was a coup against democracy."
The transitional authorities had been set to appoint liberal politician Mohamed ElBaradei, a favorite of young anti-Morsi protest leaders, before his candidacy was thrown into doubt when a hardliner Islamist party objected.
The abrupt U-turn due to opposition from the Nour Party, Egypt's second Islamist force after the Brotherhood, highlighted the challenge the military faces in finding consensus among liberals and conservatives on who should run the country and what direction they should lead it in.
"We extend our hand to everyone," a presidential spokesman told reporters late on Saturday. "The Muslim Brotherhood has plenty of opportunities to run for all elections including the coming presidential elections or the ones to follow."
Minutes after he spoke, state media reported that the public prosecutor had ordered four top Brotherhood leaders arrested this week to be detained for a further 15 days on accusations of inciting violence against protesters.
The Brotherhood has said it wants nothing to do with the military's plans for a new interim government. It wants Morsi reinstated and has pledged to keep protesting until he is.
The military has shown no sign of moving to dislodge the Islamists and may be hoping that sweltering summer heat and the onset of the Ramadan Muslim fasting month from Tuesday will gradually wear them down.
The Nour Party, the Brotherhood's rival for the Islamist vote, had agreed to the army-backed transition plan leading to new elections. Its withdrawal from the process would strip that plan of Islamist legitimacy.
For many Islamists, the overthrow of Egypt's first freely elected president was a bitter reversal that raised fears of a return to the suppression they endured for decades under autocratic rulers like Hosni Mubarak, himself toppled in the 2011 Arab Spring uprisings.
The Brotherhood called for more protests on Sunday, although by mid-afternoon they had not matched the numbers who marched two days earlier. Tahrir Square, cradle of the huge anti-Morsi movement, saw only small crowds over the weekend.
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