* After Saturday killings, U.S. warns of "pivotal moment"
* Human rights body denounces police violence
* More clashes reported in Suez Canal city
* Brotherhood says it will not back down in stand-off
The United States urged Egypt to pull "back from the brink" after security forces killed dozens of supporters of deposed President Mohamed Mursi and opened a dangerous new phase in the army's confrontation with his Muslim Brotherhood.
Thousands of Brotherhood activists were hunkered down in a vigil at a Cairo mosque on Sunday, promising to stand their ground despite Saturday's bloodshed when at least 65 pro-Mursi supporters were shot dead.
The New York-based Human Rights Watch said the killings suggested a "shocking willingness" by police and some politicians to ratchet up violence against their foes.
Backers and opponents of the ousted Islamist president clashed before dawn on Sunday in the Suez Canal city of Port Said, firing birdshot at each other before soldiers intervened, security sources said. Fifteen people were hurt in the violence.
The trouble started late on Saturday night, when gunmen fired on a church in Port Said during funeral prayers for one of the victims of the Cairo killings, the sources said.
Saturday's carnage, following huge rival rallies, plunged the Arab world's most populous country deeper into turmoil following more than two turbulent years of transition to democracy after the fall of autocrat Hosni Mubarak in 2011.
Egypt's Health Ministry said 65 people had died in the shootings, with the Brotherhood reporting that a further 61 were on life support after what it described as a ferocious assault by men in helmets and black fatigues.
The ambulance service put the death toll at 72.
Washington, treading a fine line with an important Middle East ally and recipient of more than $1 billion in annual military aid, urged the Egyptian security forces to respect the right to peaceful protest.
U.S. Defence Secretary Chuck Hagel spoke by telephone with Egyptian army chief General Abdel Fattah al-Sisi, who led the July 3 military overthrow of Mursi and whose face has since appeared on posters across the capital Cairo.
U.S. Secretary of State John Kerry spoke to two senior members of Egypt's army-installed interim cabinet, expressing his deep concern.
"This is a pivotal moment for Egypt," he said in a statement. "The United States...calls on all of Egypt's leaders across the political spectrum to act immediately to help their country take a step back from the brink."
Saturday's violence, and the threat of more, has deepened alarm in the West over events in the country of 84 million people, a vital bridge between the Middle East and North Africa.
Well over 200 people have died in violence since Sisi deposed Mursi, Egypt's first democratically-elected president, on the back of huge popular protests against his rule, ending a one-year experiment in government by the Muslim Brotherhood after decades spent in the shadows under successive Egyptian strongmen.
Mohamed Badie, the Brotherhood's leader, denounced Egypt's political establishment, saying they had failed to speak out against Saturday's killings.
"Unfortunately and shamefully, the responsibility falls on those who participated in the cover-up," he said in a statement.
Interior Minister Mohamed Ibrahim denied on Saturday that police had fired on the crowds, saying they had only used tear gas to try to break up clashes between the Brotherhood supporters and residents angry about the pro-Mursi camp.
He added that he hoped the vigil outside the Rabaa al-Adaweya mosque in northern Cairo would "God willing, soon be dealt with."
A public prosecutor is reviewing complaints from residents unhappy with the huge encampment on their doorstep.
Brotherhood spokesman Gehad El-Haddad said the protesters would remain by the mosque until their demands are met and Mursi was reinstated. He accused Sisi of issuing a "clear, pre-determined order to kill."
Saturday's killings followed a day of rival mass rallies, triggered by a call from Sisi for a popular mandate to confront what he called "violence and terrorism".
Human Rights Watch deputy Middle East and North Africa director said he thought the deaths might have been deliberate.
"It is almost impossible to imagine that so many killings would take place without an intention to kill, or at least a criminal disregard for people's lives," Nadim Houry said.
Mursi has been held in army detention at an undisclosed location since he was deposed. Ibrahim said he would likely be transferred shortly to the same Cairo prison where Mubarak is now held, after authorities launched an investigation of him on charges including murder stemming from his 2011 escape from jail during Egypt's Arab Spring uprising.