But the Muslim Brotherhood, which backs the protests, put the number of casualties much higher.
Bursts of gunfire were heard and armored bulldozers moved in. Security forces fired tear gas.
Authorities say the Nahda Square camp in western Cairo has been cleared.
The interior ministry said a mopping up operation in the surrounding streets was under way. Pro-Morsi activists were chased into the nearby zoo and Cairo University, Nile TV said.
Witnesses spoke of seeing at least 15 bodies on the ground, but the Muslim Brotherhood, describing the security forces’ intervention as a massacre, put the number of those killed at more than 100.
At least two member of the security forces were among the dead and nine were injured, officials say.
Supporters of Mohamed Morsi have been occupying Nahda Square and the site outside the Rabaa al-Adawiya mosque in the north-east of the city since he was ousted on 3 July. They want him reinstated.
Earlier, the interior ministry issued a statement saying security forces were taking “necessary measures” against the protest camps.
The statement said a safe exit would be provided for protesters and they would not be pursued, “except those who are wanted by the prosecution”.
The interior ministry is keen “not to shed any Egyptian blood”, the statement went on.
Large plumes of smoke rose over parts of the city as the operation to clear the camps began.
Muslim Brotherhood TV called for people to send cars to the sit-ins to take casualties to hospital.
An armored bulldozer was used to breach brick walls erected by the protesters outside the Rabaa al-Adawiya mosque.
Live firing was heard as the security forces moved in, our correspondent says, and police are now patrolling the nearby streets.
More than 250 people have been killed in clashes with the security forces in the six weeks since Mohamed Morsi’s overthrow.
On Tuesday, one person was killed in a confrontation between supporters and opponents of Mohamed Morsi in Giza after people marched from Nahda Square to a nearby complex of government buildings to protest against the appointment of several military officers as provincial governors.
Egypt’s Foreign Minister Nabil Fahmy said the sit-ins could not continue “endlessly”.
He said the authorities had been trying to seek an agreement through dialogue.
“If the police force take their procedures, they will do that in accordance with the law by court order and in accordance to the basic norms on which these things are done.”
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