CAIRO - At least ten people were killed in Egypt and more than 600 wounded on Sunday in clashes between supporters and opponents of Islamist President Mohamed Morsi, Israel Radio reported.
Five of the dead were shot in towns south of Cairo, one each in Beni Suef and Fayoum and three in Assiut.
Two more were killed by gunfire during an attack on the national headquarters of Morsi's Muslim Brotherhood in a suburb of the capital, medical sources said.
Hundreds of people throwing petrol bombs and rocks attacked the building, which caught fire as guards and Brotherhood members inside the building exchanged gunfire with attackers.
State news agency MENA reported that 11 were treated in hospital for birdshot wounds.
Across the country, the Health Ministry said, 613 people were injured as a result of factional fighting in the streets.
In Cairo and Alexandria, more than one million demonstrated.
Hundreds of people throwing petrol bombs and rocks attacked the national headquarters of Morsi's Muslim Brotherhood. The building caught fire as guards and protesters exchanged gunfire.
The attack came amid mass protests of hundreds of thousands of Egyptians on the first anniversary of Morsi's inauguration demanding his resignation.
Waving national flags and chanting "Get out!", a crowd of more than 200,000 had massed by sunset on Cairo's central Tahrir Square in the biggest demonstration since the 2011 uprising that overthrew Morsi's predecessor, Hosni Mubarak.
"The people want the fall of the regime!" they shouted, echoing the Arab Spring rallying cry that brought down Mubarak - this time yelling it not against an aging dictator but against the first elected leader in Egypt's 5,000 year recorded history.
Brotherhood spokesman Gehad El-Haddad said he was in contact by telephone with staff at the Muslim Brotherhood compound, who told him its fortified perimeter had not been penetrated. Several provincial offices of the movement have been attacked in recent days.
The liberal opposition National Salvation Front coalition declared victory in what it styled "Revolutionary Communique No. 1" saying the masses had "confirmed the downfall of the regime of Mohamed Morsi and the Muslim Brotherhood".
Organizers called on demonstrators to continue to occupy central squares in every city until Morsi quits. The Tahrir Square crowd roared with approval as an army helicopter hovering overhead dropped Egyptian flags on the protesters.
A military source said the move was intended to promote patriotism and was not a gesture of political support.
Many bellowed their anger at Morsi's Muslim Brotherhood, accused of hijacking the revolution and using electoral victories to monopolize power and push through Islamic law.
Others have been alienated by a deepening economic crisis and worsening personal security, aggravated by a political deadlock over which Morsi has presided.
As the working day ended and 38 Celsius (100 Fahrenheit) heat eased, more protesters converged through the eerily deserted streets of the shuttered city center, while smaller crowds protested in several other areas of the capital.
The veteran leaders of Egypt's secular, liberal and left-wing opposition, including former chief of the UN nuclear watchdog Mohamed ElBaradei and leftist presidential candidate Hamdeen Sabahi, joined protest marches in Cairo.
A Reuters journalist said hundreds of thousands of anti-government protesters marched through the Mediterranean port of Alexandria, Egypt's second city, and a military source reported protests in at least 20 towns around the country.
Morsi, an engineering professor propelled to power by the Muslim Brotherhood, was monitoring events from the heavily guarded Qubba presidential palace, where an official spokesman appealed for the demonstrations to remain peaceful.
A senior Brotherhood politician, Essam El-Erian, denounced the protests as a "coup attempt".
In a statement on the group's website, he challenged the opposition to test public opinion in parliamentary elections instead of "simply massing people in violent demonstrations, thuggery or shedding the precious blood of Egyptians".
"Maintaining the security of Egypt is the common responsibility of everyone," presidential spokesman Ehab Fahmy told a news conference. "Dialogue is the only way to reach mutual understanding and to reach national agreement around the different issues of our homeland."
Security sources said three Brotherhood offices were set on fire by demonstrators in towns in the Nile Delta - the latest in more than a week of sporadic violence in which hundreds have been hurt and several killed, including a Jewish American student.
More than 20,000 supporters of Morsi congregated outside a Cairo mosque not far from another suburban presidential palace, where protest organizers planned a sit-in from Sunday evening.
Interviewed by a British newspaper, Morsi voiced his determination to ride out what he sees as an undemocratic attack on his electoral legitimacy. But he also offered to revise the new, Islamist-inspired constitution, saying clauses on religious authority, which fueled liberal resentment, were not his choice.
He made a similar offer last week, after the head of the army issued a strong call for politicians to compromise. But the opposition dismissed it as too little to late. They hope Morsi will resign in the face of large numbers on the streets.
"We call on Mohamed Morsi, who has completely lost the legitimacy of his power, to quickly respond to the clear will of the people which is plain today in all corners of revolutionary Egypt," the June 30 movement, which organized a nationwide petition demanding his resignation, said in a statement.
Some Egyptians seem to believe the army might force the president's hand, if not to quit then at least to make major concessions to the opposition.
In Cairo, demonstrators stopped to shake hands and take photographs with soldiers guarding key buildings. At least six high-ranking police officers took to the Tahrir Square podium in support of demonstrators, a Reuters witness said.
The armed forces used military helicopters to monitor the protests in Cairo and Alexandria and a military source said chief-of-staff and Defense Minister General Abdel Fattah al-Sisi was following the situation from a special operations room.
Morsi and the Brotherhood hope the protests will fizzle like previous outbursts last December and in January. If they do not, some form of compromise, possibly arbitrated by the army, may be on the cards.
Both sides insist they plan no violence but accuse the other - and agents provocateurs from the old regime - of planning it.
The US-equipped army shows little sign of wanting power but warned last week it may have to step in if deadlocked politicians let violence slip out of control.
US President Barack Obama called for dialogue and warned trouble in the most populous Arab nation could unsettle an already turbulent region. Washington has evacuated non-essential personnel and reinforced security at diplomatic missions.
In an interview with London's Guardian newspaper, Morsi repeated accusations that what he sees as entrenched interests from the Mubarak era are plotting to foil his attempt to govern. But he dismissed the demands that he give up and resign.
If that became the norm, he said, "well, there will be people or opponents opposing the new president too, and a week or a month later, they will ask him to step down".
Liberal leaders say nearly half the voting population - 22 million people - has signed a petition calling for new elections, although there is no obvious challenger to Morsi.
The opposition, fractious and defeated in a series of ballots last year, hope that by putting millions on the streets they can force Morsi to relent and hand over to a technocrat administration that can organize new elections.
Religious authorities have warned of "civil war". The army insists it will respect the "will of the people", though the two sides have opposing views of what that means.
Islamists interpret that to mean army support for their election victories. Opponents believe that the army may heed the popular will as expressed on the streets, as it did in early 2011 when the generals decided Mubarak's time was up.
Having staged shows of force earlier this month, the Brotherhood has not called on supporters to go out on Sunday.
Among the Islamists in Cairo, Ahmed Hosny, 37, said: "I came here to say, 'We are with you Morsi, with the legitimate order and against the thugs'.
"This is our revolution and no one will take it from us."
At Tahrir Square, banners ranged from "The Revolution Goes On", "Out, Out Like Mubarak" to "Obama Backs Terrorism" - a reference to liberal anger at U.S. support for Morsi's legitimacy and criticism of protests as bad for the economy.
"I am here to bring down Morsi and the Brotherhood," said Ahmed Ali al-Badri, a feed merchant in a white robe. "Just look at this country. It's gone backwards for 20 years. There's no diesel, gasoline, electricity. Life is just too expensive."
The army, half a million strong and financed by Washington since it backed a peace treaty with Israel three decades ago, says it has deployed to protect key installations.
Among these is the Suez Canal. Cities along the waterway vital to global trade are bastions of anti-government sentiment. A bomb killed a protester in Port Said on Friday. A police general was gunned down in Sinai, close to the Israeli border.
There are some similarities with Turkey, where an Islamist prime minister with a strong electoral mandate was confronted in the streets by angry secularists this month. But Egypt is much poorer, its economy is crumbling rather than booming and its new democracy was born in a revolution just two years ago.
For many Egyptians, all the turmoil since 2011 has just made life harder. Standing by his lonely barrow at an eerily quiet downtown Cairo street market, 23-year-old Zeeka was afraid more violence was coming.
"We're not for one side or the other," he said. "What's happening now in Egypt is shameful. There is no work, thugs are everywhere ... I won't go out to any protest.
"It's nothing to do with me. I'm the tomato guy."