Hundreds of thousands of Egyptians flooded into the streets on the first anniversary of Islamist President Mohammed Mursi's inauguration today to demand that he resign.

It is the biggest challenge so far to rule by his Muslim Brotherhood.

Waving national flags and chanting "Get out!", a crowd of more than 200,000 massed on Cairo's central Tahrir Square.

It was the largest demonstration since the 2011 uprising that overthrew Mr Mursi'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.

While the main protests were peaceful, at least one Mursi supporter was shot dead and 37 people were injured in fighting in the town of Beni Suef, south of Cairo.

Dozens suffered gunshot wounds during an attack on a Muslim Brotherhood office in Housh Eissa, in the northern Nile Delta.

The Brotherhood's national headquarters in a Cairo suburb also came under attack from militants hurling petrol bombs and rocks and firing shotguns.

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 Mohammed Mursi and the Muslim Brotherhood".

Organisers called on demonstrators to continue to occupy central squares in every city until Mr Mursi 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 demonstrators bellowed their anger at the Brotherhood, which they accuse of hijacking the revolution and using electoral victories to monopolise power and impose Islamic law.

Others, including some who said they had voted for Mr Mursi, have been alienated by a deepening economic crisis and worsening personal security, aggravated by a political deadlock over which he has presided. Even some Islamists have disavowed Mr Mursi.

As the working day ended and 38C heat eased, throngs of protesters converged on Tahrir Square through the eerily shuttered city centre, while smaller crowds protested in several other locations in 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.

Mr Mursi, an engineering professor propelled from obscurity to power by the Brotherhood, was monitoring events from the heavily guarded Qubba presidential palace, where a presidency 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".

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 of people have been hurt and several killed, including an American student.

More than 20,000 supporters of Mr Mursi congregated outside a Cairo mosque not far from the main presidential palace, where a much bigger anti-Mursi sit-in swelled from the early evening.

Interviewed by a British newspaper, Mr Mursi voiced his resolve to ride out what he sees as an undemocratic attack on his electoral legitimacy.

He offered to revise the 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 too late. They hope Mr Mursi will resign in the face of large numbers on the streets.

Some Egyptians believe the army may force the president's hand, if not to quit then at least to make substantial 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 witness said.

The armed forces used 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.

Mr Mursi and the Brotherhood hope the protests will fizzle as previous outbursts did in December and January.

If 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.

The US has evacuated non-essential personnel and reinforced security at diplomatic missions.

In his interview with the Guardian newspaper, Mr Mursi repeated accusations that what he sees as entrenched interests from the Mubarak era are plotting to foil his attempt to govern.

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 Mr Mursi.

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.

To the Brotherhood, that means the result of elections. To the opposition, that means the demands of popular protests.

Having staged shows of force earlier this month, the Brotherhood did not call on its supporters to go out today.

The army, half a million strong and financed by the US 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.