The BBC's Yolande Knell said protesters were angry about the power held by the military
Two people have been killed and more than 600 injured in fierce clashes between protesters and security forces in Cairo and Alexandria.
Some protesters lobbed rocks and a police vehicle was set on fire.
The latest violence comes just over a week before parliamentary elections are scheduled to begin.
Protesters - mostly Islamists and young activists - have been holding demonstrations against a draft constitution that they say would allow the military to retain too much power after a new civilian government is elected.
Rubber bullets
Correspondents say many Egyptians are frustrated at what they see as a reluctance by the ruling military council - who took power after the fall of former President Hosni Mubarak in February - to carry out meaningful reforms.
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People here are deeply frustrated at the way the country is being run and also the prospects for the future - the very slow movement towards democracy. There are fears that the military are trying to hold onto power behind the scenes.
The big danger now is that people will lose faith in the military. The military here have always been seen as the protectors of the revolution - the guardians of the nation.
Elections are due in nine days' time. If those are blown off course by these angry demonstations, then that would blow a huge hole in the plans the military has for a handover to democracy.
Analysis
The big danger now is that people will lose faith in the military. The military here have always been seen as the protectors of the revolution - the guardians of the nation.
Elections are due in nine days' time. If those are blown off course by these angry demonstations, then that would blow a huge hole in the plans the military has for a handover to democracy.
Saturday's violence in Cairo began when police moved to dismantle tents erected by demonstrators in Cairo's Tahrir Square who had camped out for the night.
The move to clear the square prompted thousands of protesters to return, and clashes erupted. Police fired rubber bullets as cars were set on fire, witnesses said.The numbers of protesters swelled, reportedly after a call went out on social media for people to join the demonstration following the police assault.
Prime Minister Essam Sharaf called on the protesters to clear the square.
"What is happening in Tahrir is very dangerous and threatens the course of the nation and the revolution," a statement from the cabinet said.
Black smoke rose over the square after protesters swarmed over an armoured police van, turned it over and set it alight, reports said.
There were also demonstrations in Alexandria and Suez.
The state-run Mena news agency says more than 670 people were injured.
One of those wounded in Cairo later died in hospital, while a protester was killed in Alexandria during violent confrontations outside the offices of the interior ministry.
AFP quoted a security official as saying a number of arrests were made.
'Harsh beatings'
The clashes began as police moved into the square to break up a sit-in
One of the demonstrators, Ali Abdel Aziz, said security forces beat up protesters to break up the sit-in on Saturday."They beat us harshly, they didn't care for either men or women," the 32-year-old accountancy professor told AFP news agency.
"The interior ministry must take responsibility. We have one demand, the military council must go," he said.
One prominent protester, Malek Mostafa, lost an eye after being hit by a rubber bullet, said Ghada Shahbender, a member of the Egyptian Organisation for Human Rights.
"It is a crime," she told AP news agency. "They [police] were shooting rubber bullets directly at the heads... I heard an officer ordering his soldiers to aim for the head."
The interior ministry says a number of policemen were among the wounded.
In Alexandria, protester Ahmed Abdel-Qader told the Associated Press activists had thrown stones at the main security headquarters.
"We only managed to bring down the head of the regime [Hosni Mubarak]. The rest of the tree is still standing," he said.
Friday's demonstration, which saw tens of thousands fill Tahrir Square, was one of the largest for months.
Parliamentary elections are due to begin on 28 November and take three months.
Earlier this month, Egypt's military rulers produced a draft document setting out principles for a new constitution.
Under those guidelines, the military would be exempted from civilian overnight, as would its budget.
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