'How dare he talk to us like children?' say demonstrators. 'If he's here until September then so are we'

The crowd had rigged up a huge screen to show al-Jazeera. Mubarak's speech was broadcast live. As he announced that he would not be standing for another term, the rally exploded in anger.

The screen was pelted with bottles and the cry "Irhal, irhal" went up repeatedly: "Leave, leave". It was taken up by the hundred thousand people who thronged Tahrir Square. At one point demonstrators held up their shoes to the screen – an insulting gesture in Arab culture.

None of them were appeased by Mubarak's announcement. If anything, they were emboldened to step up their protests and to push their demands further. Many were saying that not only must Mubarak leave immediately but that the whole of his National Democratic party regime had to go and should be put on trial.

"If he's here until September then so are we," said Amr Gharbeia, an activist who is camping out in the square.

"Perhaps this would have been enough to appease people a few days ago but it's much too late now. He has to leave and he has to leave today," added Ibraheem Kabeel, a 26-year-old physician.

"This has only made us angrier. He must leave today. He can't wait until September. Mubarak's plane is ready," said Ahmed Defouki, a 30 year old pharmacist. "Everybody here has different opinions politically but on this issue we are united: Mubarak leaves today."

A new energy infused the crowds. People seemed more excited, sensing that they could bring Mubarak down. Another protester added: "This is the Tunisian scenario, where Ben Ali promised to stand down eventually but was quickly removed."

A prominent liberal dissident, Gamila Ismail, dismissed the president's overtures. "He gave us nothing concrete," she said. "You can't have clean elections and a fair parliament until you have a political system untainted by emergency law.

"You can't have political justice while the state security holds the political apparatus in its grip. Mubarak danced around these issues, preferring instead to show off his muscles to us. He's trying to intimidate us.

"He did not mention the citizens who have died from the bullets and bombs of his police force. This will provoke us even more. He wants this country to be burned down. This is a president playing with fireworks."

Karim Medhat Ennarah, a 27-year-old worker, said: "I watched this speech in a coffee house downtown where everybody was winding down after a long day's protest but when the speech ended the whole coffee house rose as one and began marching back to Tahrir Square. He's a man trying to bargain without realising that he has nothing left to bargain with."

Another demonstrator, Abdallah Moktar, caught the mood. "This speech has angered us much more now. How dare he talk to us like naughty children? He must go immediately," he said.

In Alexandria, however, following Mubarak's broadcast his supporters clashed with protesters occupying the main square. Sticks were brandished and rocks thrown. Bursts of gunfire were heard, thought to have been soldiers shooting into the air in an attempt to separate the two factions. There were no immediate reports of casualties.

There were similar, small-scale confrontations in central Cairo. Hundreds of pro-Mubarak activists, some on motorcycles, tried to march on Tahrir Square following the speech but were repelled by the demonstrators. Some, carrying sticks, were chanting: "We love you Hosni" and "We will defend you with our blood and souls."

Earlier hundreds of thousands of people had crammed into Tahrir Square to call for an end to Mubarak's three decades in power. Government security forces were nowhere to be seen.

The protesters hung vast banners from buildings, beat drums and chanted, they picnicked with their children on patches of scrubby grass, and walked round the square holding up vast Egyptian flags.

Most of all they called for their president to go in a multitude of different ways. "Wake up, Mubarak, this is your last day," they chanted. "We won't leave until you do."

Their banners – in Arabic, English, French and Spanish, a nod to the international audience watching this extraordinary uprising unfold – said "Game over" and "Leave now and we'll leave you alone".

Above the crowd a helicopter circled, feeding live images to Mubarak's senior security officials.

They will have seen the crush below, but not the detail in it: families and friends, bearded Islamic students, work colleagues, the rich, the middle-class and the poor putting hands on shoulders to move through the vast press of bodies in snaking lines.

They won't have seen the happy chance meetings of friends and colleagues; the intense pockets of debate about the future of the revolution that broke out on dozens of street corners; the faces lit up with the exhilaration of free expression and free assembly, as exciting as for any crowd at a football match or a rock concert. It was, as one banner had it, a festival of freedom. But what was truly extraordinary about this gathering was how far Egypt has come in a week.

People who once would not have thought of coming to protest, who would never have thought of speaking ill of a president who has ruled for 30 years or given their names to foreign journalists, have found a voice.

So they filed in their hundreds and thousands through checkpoints run by the army and checkpoints run by volunteers – who frisked all male protesters, checking their IDs to ensure that no plain clothes police officers could infiltrate the crowd. The volunteers passed out printed leaflets from soldiers asking for a peaceful assembly. Young men came with free boxes of mango juice and water to hand out, round bread and biscuits, cheese and dates. Others moved through the throng collecting litter and holding up signs for the camera.

It was a victory over fear that was assisted by a declaration from Egypt's army last night that it would not use force against those who came out on the streets today.

So they came in numbers vaster than anyone had predicted, gathering not only in the capital, but also in Alexandria, Suez and other major cities. The march of the million, Egypt's protest movement called it.

Even if it is not certain whether they reached that figure, it is clear that a transformation has taken place.

In Alexandria, at the height of the demonstration, the crowd went wild as a man in army fatigues was hoisted on to shoulders and carried into the square. He brandished his ID card and waved a national flag before the cheering masses. Was he a soldier? "Of course," said Marwa Massoud, 34. "We are the army and the people, united."

The reasons protesters gave for their presence varied only in the words they chose, not their substance. "Mubarak has lost the legitimacy of his people. It is the end of 30 years of dictatorship," said Khaled Mohammed, 52. "We want the same as every civilised nation, fair elections." A man in a wheelchair grinned and gave a thumbs-up: "Egypt! Egypt!"

A group of doctors in white coats unfurled a banner demanding the fall of the president. Almost all the signs were scrawled on cardboard ripped from cartons, a sign of a grassroots revolt. The crowd roared: "Wake up, Mubarak, today is your last day."

The streets belonged to Mubarak's opponents; those with different views kept their heads down. "Not everyone wants him out," said a taxi driver. "He's not all bad. These people are crazy."

Commenting on the military's assurances regarding protesters' security, Muhammad Warsi, a 60-year-old surgeon, in Cairo said: "The high command of the army delivered a hidden message.

"It is the same message that the elites of the country's society are delivering. They're saying [to Mubarak], 'We loved you 30 years ago. We don't want to humiliate you. We don't want you to end like [Romanian president] Nicolae Ceausescu. Go in peace.'"

Admiration for Egypt's youth was a common theme running through the crowd.

"I'm ashamed of my generation. We old people sat back and lived through decades of corruption without lifting a finger," said Aza el-Hadari, a 63-year-old bookshop owner. "This new generation has given me the best years of my life back.

"I feel sorry that Mubarak, who was after all a hero of the 1973 war effort, should be reduced to leaving with such little dignity, but he has brought this upon himself.

"Mubarak will go down in Egyptian history as the president who ordered security forces to fire live bullets into the bodies of his sons and daughters. There's no way back from that."

Mohamed Warsi was sitting on a bench waiting for his daughters, like many other recent additions to Egypt's burgeoning revolution. He told a joke doing the rounds. "OK," he says, "So Hosni Mubarak is lying on his death bed and his doctor comes and says: 'Hosni, you have to prepare a message to say goodbye to your people.' 'For my people?' asks Mubarak. 'Why? Where are the people going?'" Today the answer came – to Tahrir Square, to bid their president of 30 years goodbye.