A court ordered Morsi held for 15 days while allegations he colluded with Hamas are investigated, Ahram Online reported. Morsi is accused of collaborating with the militant Palestinian organization to escape from Wadi el-Natroun Prison and destroy prison records during Egypt's 2011 uprising. He's also accused of working with Hamas to attack police stations during the uprising, the intentional killing and kidnapping of police officers and prisoners, and espionage, the BBC said.
Morsi has been held at an undisclosed location since he was ousted by the military.
High-ranking military officers joined a large crowd of anti-Morsi demonstrators in Tahrir Square in Cairo, Ahram said.
Abdel Fattah el-Sisi, the head of the military and defense minister, had urged crowds to come out to give the military a mandate.
"The Army, the police and the people are one hand," many in the crowd chanted.
The detention is seen by some as a legal way to keep Morsi in prison until proper charges are filed against him, the BBC said.
Egypt braced for bloodshed Friday in rallies for and against the military that ousted Morsi.
The army vowed to shoot protesters committing violent acts.
The grand imam of al-Azhar, considered by some Muslims the highest authority in Sunni Islamic thought, urged rival protesters to remain peaceful, amid vows from both sides for a decisive struggle in Cairo's streets.
Morsi was ousted July 3 by Sisi, 11 months after Morsi appointed him commander in chief and defense minister.
"I urge the people to take to the streets ... to prove their will and give me, the army and police a mandate to confront possible violence and terrorism," Sisi said Wednesday in a televised address.
Sisi asked people to refrain from violence in protests, Friday, the same day Morsi's mostly Islamist supporters planned about 34 marches in Cairo.
The army said on Facebook Thursday it would not turn its guns "against its people" but would readily shoot those committing "violence and terrorism, which has no religion or nation."
The military increasingly refers to Muslim Brotherhood members, who support Morsi, as "terrorists."
The brotherhood accused military-led authorities of stoking violence to legitimize an anti-brotherhood crackdown ever since Morsi's ouster. The brotherhood said Sisi and the military have a final goal of eliminating the Islamist religious, political and social movement, which was illegal in Egypt until after the 2011 overthrow of President Hosni Mubarak.
The military has asked the brotherhood to end its opposition and join a military-designed road map it promises will lead to parliamentary elections in February. The brotherhood has refused, calling the government the military created illegitimate.
The White House expressed concern about possible Friday violence.
"The Obama administration is concerned by any rhetoric that inflames tensions and could possibly lead to more violence," White House spokesman Josh Earnest told reporters aboard Air Force One Thursday.
"This is a critical time for Egyptians to come together if they want to -- particularly if they want to move beyond cycles of unrest and instability," Earnest said.
He said the administration urged security forces "to exercise maximum restraint and caution, and to do their utmost to prevent any clashes between opposing demonstrators -- and we reiterate our call for protesters to demonstrate peacefully."