It was unclear from the general’s statement whether the military was specifically demanding that Mr. Morsi resign. But the statement said that if Mr. Morsi did not take steps to address demands for a more inclusive government, the armed forces would move to impose its “own road map for the future.”
The Health Ministry said on Monday that 16 people had died in the protests, including eight in the battle outside the Muslim Brotherhood headquarters, most of them from gunshot wounds. All of those killed outside the headquarters were young, including one who was 14 and another who 19, the ministry said. One died of heat-related causes at a demonstration outside the presidential palace.
After dawn broke Monday, some demonstrators remained in Tahrir Square, resting under impromptu shelters. While much of the protest elsewhere in Cairo seemed peaceful, activists reported dozens of sexual assaults on women in Tahrir Square overnight.
The fiercest confrontation seemed to be at the Brotherhood headquarters where members of the organization who were trapped inside fired bursts of birdshot at the attackers and wounded several of them.
After pelting the almost-empty building for hours with stones, Molotov cocktails and fireworks, the attackers doused its logo with kerosene and set it on fire, witnesses said, seeming to throw what appeared to be sandbags used to fortify the windows out onto the street.
It was not immediately clear what became of the Brotherhood members, but shortly before the building was stormed, armored government vehicles were seen in the area, possibly as part of an evacuation team.
News reports on Monday spoke of fatalities across the nation numbering around 16.
The scale of the demonstrations, just one year after crowds in the same square cheered Mr. Morsi’s inauguration, appeared to exceed even the mass street protests in the heady final days of the uprising that overthrew President Hosni Mubarak in 2011. At a moment when Mr. Morsi is still struggling to control the bureaucracy and just beginning to build public support for painful economic reforms, the protests have raised new hurdles to his ability to lead the country as well as new questions about Egypt’s path to stability.
Clashes between Mr. Morsi’s opponents and supporters broke out in several cities around the country, killing at least seven people — one in the southern town of Beni Suef, four in the southern town of Assiut and two in Cairo — and injuring hundreds. Protesters ransacked Brotherhood offices around the country.
Demonstrators said they were angry about the lack of public security, the desperate state of the Egyptian economy and an increase in sectarian tensions. But the common denominator across the country was the conviction that Mr. Morsi had failed to transcend his roots in the Brotherhood, an insular Islamist group officially outlawed under Mr. Mubarak that is now considered Egypt’s most formidable political force.
The scale of the protests across the country delivered a sharp rebuke to the group’s claim that its victories in Egypt’s newly open parliamentary and presidential elections gave it a mandate to speak for most Egyptians.
“Enough is enough,” said Alaa al-Aswany, a prominent Egyptian writer who was among the many at the protests who had supported the president just a year ago. “It has been decided for Mr. Morsi. Now, we are waiting for him to understand.”
Shadi Hamid, a researcher at the Brookings Doha Center in Qatar who studies the Muslim Brotherhood closely, said: “The Brotherhood underestimated its opposition.” He added: “This is going to be a real moment of truth for the Brotherhood.”
Mr. Morsi and Brotherhood leaders have often ascribed much of the opposition in the streets to a conspiracy led by Mubarak-era political and financial elites determined to bring them down, and they have resisted concessions in the belief that the opposition’s only real motive is the Brotherhood’s defeat. But no conspiracy can bring millions to the streets, and by Sunday night some analysts said the protests would send a message to other Islamist groups around the region in the aftermath of the Arab Spring.
“It is a cautionary note: Don’t be too eager for power, and try to think how you do it,” Mr. Hamid said, faulting the Egyptian Brotherhood for seeking to take most of the power for itself all at once. “I hear concern from Islamists around the region about how the Brotherhood is tainting Islamism.”
Mr. Morsi’s administration appeared caught by surprise. “There are protests; this is a reality,” Omar Amer, a spokesman for the president, said at a midnight news conference. “We don’t underestimate the scale of the protests, and we don’t underestimate the scale of the demands.” He said the administration was open to discussing any demands consistent with the Constitution, but he also seemed exasperated, sputtering questions back at the journalists. “Do you have a better idea? Do you have an initiative?” he asked. “Suggest a solution and we’re willing to consider it seriously.”
Many vowed to stay in the streets until Mr. Morsi resigned. Some joked that it should be comparatively easy: Just two years ago, Egyptian protesters toppled a more powerful president, even though he controlled a fearsome police state. But there is no legal mechanism to remove Mr. Morsi until the election of a new Parliament, expected later this year, and even some critics acknowledge that forcing the first democratically elected president from power would set a precedent for future instability.
Some of the protesters called for another intervention by the military, which seized power from Mr. Mubarak and held onto it for more than a year. Chants were directed to the defense minister, Gen. Abdul-Fattah el-Sisi: “Come on Sisi, make a decision!”
General Sisi, for his part, has stayed carefully neutral, feeding the protesters’ hopes. In a statement last week urging the president and his opponents to compromise, the general said the military would “intervene to keep Egypt from sliding into a dark tunnel of conflict, internal fighting, criminality, accusations of treason, sectarian discord and the collapse of state institutions.”
Many in the opposition saw the statement as an indication that if the protests Sunday were disruptive enough, the military would take over once again. The military sent four helicopters flying low over a demonstration in Tahrir Square in Cairo on Sunday to reinforce its power and control, and many below cheered.
The Web site of the flagship state newspaper, Al Ahram, reported Sunday that soldiers had been ordered only to “protect the will of the people without bias to any side at the expense of the other, especially as the political forces have not reached any formula of consensus.”
The extrication of the military from power was the biggest achievement of Mr. Morsi’s first year in office. Last August, months after his election, the generals finally went back to their barracks and allowed him to take full power as president, although the military retains considerable autonomy under Egypt’s new Constitution.
But Mr. Morsi continued to battle institutions within his own government left over from Mr. Mubarak, most notably the judiciary, and some of those fights contributed to the protests that peaked Sunday. The protests began in November, when he tried to declare himself above the courts until the passage of a new Constitution, a move that reinforced the fears of his opponents and perhaps the general public that he threatened to become a new autocrat.
“He was of the revolution,” said Magdi Morsi, an airline flight planner demonstrating in front of the presidential palace who is not related to the president. He said he had voted for Brotherhood candidates for Parliament as well as for Mr. Morsi but had turned against them for failing to deliver on their promises. “I decided he was a big liar,” he said. “He must leave. The public is against him now.”
The police, another institution left intact from the Mubarak government, are in open revolt against Mr. Morsi. In anticipation of the protests Sunday, the interior minister had already announced that the police would not protect the offices of the Muslim Brotherhood from attack. And when the protests began, police officers were almost nowhere to be found.
Several officers in uniform joined the protesters in Tahrir Square calling for Mr. Morsi’s ouster and asking the military to intervene. Two officers were seen in the vicinity of the attack on the Brotherhood’s headquarters talking on hand-held radios, but they did nothing to intervene.
Two armored vehicles from the interior security forces later arrived but also did nothing to stop the attack. The officers listened for a while as the attackers appealed to them to arrest the few Brotherhood members trying to defend their headquarters with birdshot, and then they left.
The attackers used green pen lasers to search for figures at the windows of the Brotherhood offices, then hurled Molotov cocktails. They vowed to show no mercy on the members inside. “Their leaders have left them like sheeps for the slaughter,” one said. Two people were killed in the violence at the headquarters, medics there said.
Thousands of Mr. Morsi’s supporters in the Muslim Brotherhood had gathered at a rally near the presidential palace to prepare to defend it if the protesters tried to attack. Many brought batons, pipes, bats, hard hats or motorcycle helmets, even woks or scraps of metal to use as shields. They stood at attention with clubs raised and marched together. “We will sacrifice our lives for our religion,” some chanted. “Morsi’s men are everywhere.”
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By DAVID D. KIRKPATRICK, KAREEM FAHIM and BEN HUBBARD. Mayy El Sheikh contributed reporting. The New York Times