Those protests again turned violent Monday, with clashes breaking out between Morsi supporters and opponents near Cairo's Tahrir Square, and between pro-Morsi demonstrators and police in a city on the capital's northern edge. At least four people were killed.
So far, however, the outcry over Morsi's detention seems to have gained little traction beyond the president's supporters, without bringing significantly greater numbers to its ongoing rallies around the country.
Millions of Egyptians filled the streets starting June 30, demanding the president's removal after a year in office and leading to the coup that ousted him. Anti-Brotherhood sentiment remains strong, further fueled by protests that block traffic in congested city centers and by media that have kept a staunchly anti-Morsi line. Egyptian human rights groups have said he should either be freed or charged.
Behind-the-scenes talks have been taking place through mediators between Brotherhood figures and the interim government centered around releasing Morsi and other detained leaders of the group in return for an end to protests by his supporters, according to Mohammed Aboul-Ghar, head of a liberal political party that backed the president's overthrow.
The military fears that Morsi's release "would only increase protests and make them more aggressive," he told The Associated Press. At least five other prominent Brotherhood members have also been detained. The military also has said that there is no way the measures taken against Morsi will be reversed.
The Brotherhood so far seems unlikely to make a deal, saying it cannot accept a military coup. It and other Morsi supporters vow they will not stop protests until he is returned to office, and they have said there will be no negotiations with the new leadership unless it accepts his reinstatement. They have denied any back-channel talks are taking place.
In a toughly worded statement Monday, the Brotherhood laid out a plan for resolving the crisis that was little changed from what Morsi proposed in his final days in office. It said Morsi must first be reinstated along with the now-dissolved upper house of parliament and the suspended constitution, followed by new parliament elections that would start a process for amending the constitution, and then a "national dialogue" could be held.
It denounced those behind Morsi's ouster as "putschists" and accused "coup commanders, with foreign support" of overthrowing "all the hopes in a democratic system."
Interim President Adly Mansour repeated calls for reconciliation in a nationally televised speech Monday evening. "We ... want to turn a new page in the nation's book," he said. "No contempt, no hatred, no divisions and no collisions."
Morsi was detained July 3, when Gen. Abdel-Fattah el-Sissi, the army chief, announced his removal. He is held at an undisclosed location and has had no contact with family or supporters. Government officials have said only that he is safe, is well-cared for and is being held for his own protection.
Two of Morsi's children lashed out at the military over his detention, saying his family has not been permitted to see him since then.
"What happened is a crime of kidnapping," one of his sons, Osama, told a Cairo news conference. "I can't find any legal means to have access to him."
The younger Morsi, who is a lawyer, called his father's detention the "embodiment of the abduction of popular will and a whole nation," and said the family will "take all legal actions" to end his detention.
In a statement read by Morsi's daughter, Shaimaa, the family said it held "the leaders of the bloody military coup fully responsible for the safety and security of the president."
European Union foreign ministers called for the release of Morsi and "all political detainees," saying it was among their key priorities for Egypt's new leadership.
The United States has stopped short of calling for his release. The White House repeated its call Monday for the end of politicized arrests and detentions. But spokesman Jay Carney said of Morsi: "We believe his situation needs to be resolved in a way that is consistent with the rule of law and due process and allows for his personal security."
"This is an issue that goes beyond one individual," he said, adding that resolving Morsi's situation wouldn't end the broader conflict in Egypt.
Prosecutors have said they are investigating allegations that Morsi and Brotherhood officials conspired with the Palestinian militant group Hamas to carry out a 2011 attack on prisons that freed Morsi and other Brotherhood leaders from jail during the 18-day uprising against autocrat Hosni Mubarak.
However, the prosecutors have not formally ordered Morsi detained for investigation, meaning his detention effectively remains outside the legal system.
Prominent rights activist Hossam Bahgat said a coalition of rights groups are preparing a joint call for Morsi to be indicted over the deaths of dozens of Egyptians in street riots and protests under his rule.
More than 40 people were killed in January in clashes with security forces. A month earlier, 10 others were killed when supporters of the Muslim Brotherhood clamped down on anti-Morsi protesters staging a sit-in in front of the presidential palace. Several activists, arrested in street protests, were killed during torture.
But Bahgat noted that charges on those deaths would put the new leadership in a difficult position because it would also require indicting the current interior minister, in charge of police, who held the post under Morsi as well.
Instead, authorities are turning to "more politicized cases," said Bahgat, director of the Egyptian Initiative for Personal Rights. "All what is circulating now is more of a fiction than real."
"Now he is being held hostage to political negotiations and it depends on the deal, his fate will be decided."
Morsi's supporters have been holding protests and street marches nearly every day in Cairo in addition to sit-ins that have gone on for weeks in several cities. The marches have repeatedly turned violent, with dozens of mostly Morsi supporters killed.
Abdel-Sattar el-Meligi, a prominent former Brotherhood figure, said the group is hoping that protests can rally wider popular support. So far, however, "these are just very desperate attempts," he said.
"The Brotherhood failed to estimate the real anger in the street, the political weight of their opponents," he said. "The Brotherhood has exhausted all their credit in all levels."
On Monday, Essam el-Erian, deputy head of the Brotherhood's political party, urged protesters to "besiege" the U.S. Embassy and expel the ambassador, stepping up the group's accusations that Washington backed the coup. Morsi's opponents, in turn, accuse the U.S. of supporting his presidency.
Several hundred Islamists tried to march toward the U.S. Embassy hours later, passing near Tahrir Square, where Morsi opponents have been camped. Rock-throwing clashes erupted between the two sides, and gunshots were heard, though it was not clear who opened fire. Both sides were seen to have what appeared to be homemade pistols.
One Morsi opponent was killed and dozens of others wounded, some by birdshot and two by live ammunition, said George Ihab, a doctor at a field clinic set up by the anti-Morsi camp.
Several anti-Morsi demonstrators said the ousted president's supporters attacked their people guarding an entrance to Tahrir near a bridge over the Nile River.
"They attacked us from Qasr el-Nil Bridge with birdshot and live ammunition and molotovs," said Ahmed Korashi, whose hand was burned from what he said was a firebomb.
In a tweet, the Muslim Brotherhood denied its supporters attacked, saying its protests are peaceful.
Clashes also broke out in Qalioub, north of Cairo, when pro-Morsi protesters blocked a highway between the capital and the Mediterranean coastal city of Alexandria, security officials said. The security forces demanded the road be cleared, and protesters fired ammunition in the air. Clashes erupted with protesters throwing stones and security forces firing tear gas.
At least three people were killed, including a 15-year-old and an 18-year-old who died of gunshot wounds, the officials said, speaking on condition of anonymity because they were not authorized to talk to the press.
Security officials said the body of a 33-year-old textile worker, Amr Magdy Samak, was found near the sit-in with signs of torture. His body had bruises and his nails had been torn off, the officials said, adding that the death was under investigation.
In the Sinai Peninsula, suspected Islamic militants attacked security checkpoints in the town of Sheikh Zuweyid and the nearby city of el-Arish, killing a civilian and wounding three soldiers, security officials said. A string of militant attacks in the Sinai since Morsi's fall has killed 14 members of the security forces and several civilians.