* Protesters shot in early hours near pro-Mursi vigil
* Violence erupts after rival rallies across Egypt
* Army chief had called for mandate to tackle "terrorism"
Egyptian security forces shot dead dozens of supporters of ousted Islamist President Mohamed Mursi on Saturday, witnesses said, days after the army chief called for a popular mandate to wipe out "violence and terrorism".
Men in helmets and black police fatigues fired on crowds gathered before dawn on the fringes of a round-the-clock sit-in near a mosque in northeast Cairo, Mursi's Muslim Brotherhood said.
"They are not shooting to wound, they are shooting to kill," said Brotherhood spokesman Gehad El-Haddad. "The bullet wounds are in the head and chest."
A Muslim Brotherhood website said 120 people had been killed and some 4,500 injured. A Reuters reporter counted 36 bodies at one morgue, while health officials said there were a further 21 corspes in two nearby hospitals.
Activists rushed blood-spattered casualties into a makeshift hospital, some were carried in on planks or blankets. One ashen teenager was laid out on the floor, a bullet hole in his head.
Egypt's Interior Minister Mohamed Ibrahim told reporters only 21 had died and denied police had opened fire, accusing the Brotherhood of exaggerating for political ends.
Ibrahim 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 road bridge. He said that 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 July 3, following huge protests against his year in power. The army denies accusations it staged a coup, saying it intervened to prevent national chaos.
The Arab world's most populous state is battling economic woes and struggling with the transition to democracy two years after Hosni Mubarak was swept from power in the Arab Spring.
Hundreds of thousands of Egyptians had poured onto the streets on Friday in response to a call by army chief General Abdel Fattah al-Sisi for nationwide demonstrations to give him backing to confront the weeks-long wave of violence.
His appeal was seen as a challenge to the Brotherhood, which organised its own rallies on Friday calling for the return of Mursi, who has been held in an undisclosed location since his ousting and faces a raft of charges, including murder.
Brotherhood leaders appealed for calm on Saturday, but activists at the Rabaa al-Adawia mosque vigil voiced fury.
"The people want the execution of Sisi," a cleric shouted to the crowd from a stage by the mosque. "The people want the execution of the butcher."
Interior Minister Ibrahim said the pro-Mursi sit-ins would "God willing, soon ... be dealt with" based on a decision by a public prosecutor, who is reviewing complaints from local residents unhappy with the huge encampment on their doorstep.
The Brotherhood is a highly organised movement with grassroots support throughout Egypt, making it hard to silence even if the army decides to mount a bigger crackdown.
European Union foreign policy chief Catherine Ashton said she "deeply deplores" Saturday's deaths and urged all sides to halt the violence. There was no immediate comment from the United States, which provides Egypt with some $1.5 billion dollars of aid a year, mainly military hardware.
Washington has delayed delivery of four F-16 fighters because of the turmoil, however, officials have indicated they do not intend to cut off aid to a country seen as a vital ally and which has a peace deal with neighbouring Israel.
Witnesses said police first fired rounds of teargas at Brotherhood protesters gathered on a boulevard leading away from the Rabaa mosque, with live shots ringing out soon afterwards.
"There were snipers on the rooftops, I could hear the bullets whizzing past me," said Ahmed el Nashar, 34, a business consultant, choking back his tears.
"Man, people were just dropping."
Dr. Ibtisam Zein, overseeing the Brotherhood morgue, said most of the dead were hit in the head, some between the eyes.
The bodies were wrapped in white sheets and laid on the floor, their names scrawled on the shrouds. A cleaner busily mopped the floor, washing away pools of blood.
Haddad said the Brotherhood remained committed to pursuing peaceful protests, despite Saturday's deaths - the second mass shooting of its supporters this month by security forces, who killed 53 people on July 8.
Brotherhood activists at Rabaa said they would not be cowed and warned of worse bloodshed if the security forces did not back down. "We will stay here until we die, one by one," said Ahmed Ali, 24, helping treat casualties at the field hospital.
"We have the examples of Algeria and Syria in our minds. We don't want it to become a civil war. If we take up arms it might become one. This is a religious belief."
There was little mention of the violence on Egypt's two state television channels, which broadcast weather reports and a talk show on Saturday morning. All three state newspapers headlined their morning editions with Friday's rallies, saying Egyptians had given Sisi the support he had asked for.
"The people give the army and the police a mandate to confront terrorism," said a strap headline on the bottom of a broadcast on the state's Nile TV.
Ibrahim said Mursi, who has not been seen in public since his removal from power, was likely to be transferred shortly to the same Cairo prison where former leader Mubarak is now held.