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Human Rights Watch said many of those killed over the weekend were shot in the head or chest and the killings took place over several hours. The New York-based group said it had spoken with witnesses and reviewed extensive video footage of the events. Medical staff, it said, judged some of the deaths to be targeted killings because the position of the shots likely would result in death.

The clashes broke out hours after millions responded to a call by Gen. Abdel-Fattah el-Sissi, the military chief, to take to the streets in a show of support to provide a mandate for him and the police to tackle violence and “potential terrorism.”

Two other men were killed and scores injured in violence that followed the funerals of two Morsi supporters Sunday in two cities north of Cairo, Kafr el-Zayat and Port Said.

Mohammed Badie, the supreme leader of the Mr. Morsi’s Muslim Brotherhood, launched a stinging attack on Gen. el-Sissi over the latest violence, saying the military chief was leading a “bloody regime” and urging his followers to stand fast.

“Don’t be sad and don’t despair,” he said in a message to followers posted on his website.

The Brotherhood rejects the July 3 coup, saying it overturned a democratically elected administration, and refuses to join the post-Morsi political process sponsored by the military. It says security forces were not provoked when they opened fire on its supporters early  Saturday.

Interior Minister Mohammed Ibrahim, who is the only member of Mr. Morsi’s former Cabinet to keep his post, accused the pro-Morsi side of provoking bloodshed to win sympathy and suggested that authorities could move against the two main pro-Morsi protest camps: one outside the Rabaah al-Adawiya Mosque in eastern Cairo and another in Nahda Square near the main campus of Cairo University.

“I assure the glorious people of Egypt that the police are determined and capable to maintain security and safety to their nation with the support of the sincere sons of the country,” Mr. Ibrahim said Sunday during a graduation ceremony at the national police academy. “We will very strongly and decisively deal with anyone who attempts to undermine stability.”

He depicted the two encampments as a danger to the public, pointing to a string of nine bodies that police have said were found nearby in recent days. Some were tortured to death, police said, apparently by members of the sit-ins who believed they were spies.

“Soon we will deal with both sit-ins,” Mr. Ibrahim said.

U.N. Secretary-General Ban Ki-moon also asked security forces to “act with full respect for human rights” and demonstrators to “exercise restraint.”

Catherine Ashton, the European Union’s foreign policy chief, was due in Egypt later on Sunday and will meet Egyptian leaders on Monday, according to an official statement issued in Cairo. It will be her second visit to Egypt this month, a sign of the alarm felt in the West over the continuing bloodshed in the country.

The U.N.’s human rights chief, Navi Pillay, also condemned the violence and called for a “credible, independent investigation” into the killings.

“Despite all the warnings, all the calls for restraint, more than 150 Egyptians have died during protests over the past month, not just in Cairo but in other cities as well,” Mrs. Pillay said. “I fear for the future of Egypt if the military and other security forces, as well as some demonstrators, continue to take such a confrontational and aggressive approach. Supporters of the Muslim Brotherhood have the right to protest peacefully like anyone else.”

• Associated Press writers Maggie Michael in Cairo and Frank Jordans in Berlin contributed to this article.