"May God bring Morsi back to power," and "May God end the rift between us and the army," the imam leading the prayer told worshippers at the Rabaa al-Adawiya mosque.
Ahead of the rallies, around a dozen low-flying military jets screeched across Cairo.
The call for "peaceful protests" across Egypt came from the Brotherhood's recently formed National Alliance to Support Legitimacy, which it said were against "the military coup" and in support of Morsi.
The deposed leader, who has not been seen since Wednesday, had issued a defiant call for supporters to protect his elected "legitimacy", in a recorded speech hours after he was toppled.
With thousands of Morsi supporters camped outside the Rabaa al-Adawiya mosque encircled by military vehicles, the call for demonstrations raised fears of fresh violence after days of bloodshed.
The military said it supported the right to peaceful protest, but warned against violence and acts of civil disobedience such as blocking roads.
Human Rights Watch called for "prompt, impartial investigations to determine who was responsible for killings" since late June.
"The available information indicates that both supporters and opponents of Morsi -- and possibly security forces as well -- were responsible for needless loss of life," said HRW's Joe Stork.
In the Sinai, militants killed a soldier early Friday, as gunmen ambushed army and police positions with machineguns and rockets.
State news agency MENA said military Apache helicopters struck a militant's vehicle in pursuit of gunmen who attacked an airport in the north of the restive peninsula.
The army boosted security in the peninsula in response, officials said.
Some militants in the Sinai had threatened a violent response after Morsi's ouster on Wednesday.
Clashes also broke out in the Nile Delta province of Sharqiya, hours after chief justice Adly Mansour, was sworn in on Thursday as interim president until new elections.
The army warned Egyptians against resorting to "exceptional and autocratic measures against any political group".