Protesters in front of the El-Thadiya presidential palace in Cairo.

Hundreds of thousands of Egyptians flooded into the streets on the first anniversary of Islamist President Mohamed Morsi’s inauguration yesterday to demand that he resign.

One person was killed and more than two dozen injured in fighting between supporters and opponents of Morsi in the Nile city of Beni Suef, south of Cairo, security sources said. Egypt's ruling Muslim Brotherhood said its Cairo headquarters came under attack from scores of anti-government protesters firing shotguns and throwing petrol bombs and rocks.

Brotherhood spokesman Gehad El-Haddad said he was in contact by telephone with staff at the compound, who told him its fortified perimeter had not been penetrated. Several provincial offices of the movement have been attacked in recent days.

Two men, including an American bystander, were killed when the Brotherhood's office in Alexandria, Egypt's second city, was attacked on Friday and dozens were wounded. The office was torched and ransacked.

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 ageing dictator but against the first elected leader in Egypt’s 5,000-year recorded history.

Many bellowed their anger at Morsi’s Muslim Brotherhood, accused of hijacking the revolution and using electoral victories to monopolise 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 heat eased, more protesters converged through the eerily deserted streets of the shuttered city centre, 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.

“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 an American student.

More than 20,000 supporters of Morsi congregated outside a Cairo mosque not far from another suburban presidential palace, where protest organisers planned a sit-in from Sunday evening.

Protesters shouting anti-Morsi slogans in Tahrir Square yesterday.

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 fuelled 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 organised 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 Defence 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 organise new elections.