The move sparked days of nationwide violence that killed more than 1,000 people, most of them Morsi's supporters. Many retaliated by attacking police stations, torching churches and setting government buildings on fire.
In an interview Thursday with The Associated Press, a leader of the Gamaa Islamiya ex-militant group, Abboud el-Zommor, urged both Muslim Brotherhood and military to make "concessions" and acknowledged that both are responsible for the bloodshed.
"There were miscalculations," he said about the Brotherhood alliance refusing to disband the sit-in before state crackdown. "I knew there would be losses of many lives and I wanted to find a political exit.
Gamaa Islamiya is one of two former militant groups who have offered an initiative to halt the country's political violence
El-Zommor said he met with military generals and Brotherhood members who both welcomed his call to take measures to stop escalations. He suggested that the Brotherhood's attempt to escalate protests might be a way to improve their position ahead of any possible negotiations with the government.
Under his proposed plan, the government would lift the state of emergency, stop mass arrests of Islamists and offer assurances that Islamists wouldn't be excluded in future elections. In return, he said the Brotherhood would have to promise to hold only "peaceful protests" and not attack churches or state institutions.
"We noticed that the military is willing to find an exit knowing the dangers of continuation of the struggle," el-Zommor said. "It could lead to destruction of the nation."
The Brotherhood, once Egypt's most powerful political group, has been weakened by mass arrests of hundreds of top and midlevel leaders. Police also have gone after members' relatives.
State television and police officials said Thursday that officers arrested outspoken former Brotherhood lawmaker Mohammed el-Beltagy and former Labor Minister Khaled el-Azhari. Both are wanted by police for allegedly inciting violence. El-Beltagy is also wanted over alleged involvement in an assault on a police officer kidnapped by protesters at the main Cairo sit-in before it was cleared.
El-Beltagy was among four top Islamists who took to the airwaves in the past 24 hours to try and whip up support for Friday's protests after a week of small and scattered rallies. They called on people to stand their ground against the "failed, bloody military regime."
The Interior Ministry, in charge of police, said in a nationally televised statement Thursday that its forces would deal with "firmness" against acts that threaten national security and that police had orders to use deadly force in defense of public and private property. The ministry said that the Brotherhood's calls are aimed at stirring chaos. A nighttime curfew in Cairo and 13 other provinces will start earlier on Friday at 7 p.m. and end 6 a.m.
The Brotherhood released a four-page Arabic statement Thursday, part of which called on security forces to disobey orders "to kill." The group and their supporters have flashed four fingers and used it as their symbol in online and street campaigns for protests. It comes from the sit-in around Rabaa el-Adawiyah mosque, which in Arabic means fourth.
A photo purporting to show el-Beltagy just after his arrest has him flashing the sign and smiling between two masked policemen.
The pre-recorded Brotherhood messages all aired on Al-Jazeera Mubasher Misr, an affiliate of the Qatar-based broadcaster. Egypt's interim government on Thursday deemed the local Al-Jazeera affiliate a national threat, moving closer to banning its broadcast. It is among the only channels seen as sympathetic to the Brotherhood still broadcasting after others were ordered closed.
The television network later said four journalists working for its English service were arrested in Cairo.