* 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"
* United States warns Egypt at "pivotal moment" (Updates with U.S. reaction)
By Tom Perry and Shadia Nasralla
CAIRO, July 27 (Reuters) - 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".
The bloodshed, near the military parade ground where President Anwar Sadat was assassinated in 1981, plunged the Arab world's most populous country deeper into turmoil following two turbulent years of transition to democracy since veteran autocrat Hosni Mubarak was swept from power.
Mursi's Muslim Brotherhood, braced for a military crackdown, said men in helmets and black police fatigues had fired on crowds gathered before dawn on the fringes of a round-the-clock sit-in near a mosque in northeast Cairo.
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.
The United States, treading a fine line with an important Arab ally and recipient of over $1 billion a year in U.S. military aid, urged respect for the right to peaceful protest, and warned that Egypt was at a "pivotal moment".
Brotherhood spokesman Ahmed Aref said 66 people had been killed and another 61 were "brain dead" on life support machines. More than 4,000 were treated for the effects of tear gas and gunshot or birdshot wounds, he told reporters.
"Innocent blood was spilled," 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, saying 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 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.
SISI'S CHALLENGE
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.
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 on Saturday, but activists at the 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 European Union and major European powers deplored the violence. U.S. Secretary of State John Kerry urged dialogue and restraint.
"At this critical juncture, it is essential that the security forces and the interim government respect the right of peaceful protest," he said. "This is a pivotal moment for Egypt."
Washington has delayed delivery of four F-16 fighters, part of the $1.5 billion in aid it provides every year, mainly in military hardware, but says it does not intend to cut off aid to a country seen as a vital ally and which has a peace deal with neighbouring Israel.
"BULLETS WHIZZING"
Turkey, a vocal supporter of Mursi, accused the West of turning a blind eye. "Those who were silent when Egypt's national will was massacred are silent again when people are massacred," Prime Minister Tayyip Erdogan, who has faced down large protests against his own government this year, said in televised comments.
"What happened to the EU (and) European values, where are those who go around giving lessons in democracy?"
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.
The influential Sheikh Ahmed al-Tayeb, head of Egypt's top Islamic institute Al-Azhar, said there would be worse to come without a settlement, in comments carried by the MENA state news agency. "The only alternative to dialogue is destruction," he said. (Additional reporting by Shadia Nasralla, Yasmine Saleh, Tom Finn, Maggie Fick, Omar Fahmy, Edmund Blair, Michael Georgy, Noah Browning and Ahmed Tolba in Cairo, Abdel Rahman Youssef in Alexandria, Arshad Mohammed in Washington and Ayla Jean Yackley in Istanbul; Writing by Crispian Balmer; and Matt Robinson and David Evans)
Our Standards: The Thomson Reuters Trust Principles.
