The United States has urged Egypt to respect the right to peaceful protest, and warned that Egypt was at a "pivotal moment".
Muslim Brotherhood spokesman Ahmed Aref said 66 people had been killed and another 61 were "brain dead" on life support machines.
More than 4,000 people were treated for the effects of teargas and gunshot or birdshot wounds.
"Innocent blood was spilled," Mr Aref said. "We have gone back 10 years."
The Health Ministry reported a total of 65 dead, while the head of the ambulance service, Mohamed Sultanm, said later that 72 had died.
"They are not shooting to wound, they are shooting to kill," another Brotherhood spokesman, Gehad El-Haddad, told Reuters early on Saturday. "The bullet wounds are in the head and chest."
Egypt's Interior Minister Mohamed Ibrahim denied that police had opened fire.
He said local residents living close to the Rabaa al-Adawia mosque vigil had clashed with protesters in the early hours after they had blocked off a major bridge road.
He said police had used teargas to try to break up the fighting.
Well over 200 people have been killed in violence since the army toppled Mursi on 3 July , following huge protests against his year in power.
The army denies accusations it staged a coup, saying it intervened to prevent national chaos.
Hundreds of thousands of Egyptians had poured onto the streets yesterday in response to a call by army chief General Abdel Fattah al-Sisi for nationwide demonstrations.
He called for the backing to confront the weeks-long wave of violence.
His appeal was seen as a challenge to the Muslim Brotherhood, which organised its own rallies on yesterday calling for the return of Mr Mursi.
Mr Mursi has been held in an undisclosed location since his ousting and faces a raft of charges, including murder.
Mr Ibrahim said Mursi was likely to be transferred shortly to the same Cairo prison where former leader Mubarak is now held.
Leaders of the Brotherhood, a highly organised movement with grassroots support across Egypt, appealed for calm today, but activists at the vigil voiced fury.