Several arrests were made, Today's Zaman reported.
The demonstrations began during the weekend, mainly in the southeast. One protester was killed by police Monday in Dogubeyazit.
Ocalan, who was sentenced to life in prison, is being held on Imrali, an island in the Sea of Marmara.
Ocalan's attorneys say the leader of the Kurdistan Workers Party, often referred to as the PKK, was beaten when he objected to a destructive search of his cell, Bianet reported. They also charge that his guards threatened him by responding "In good time" when he said they "might as well kill him."
In another incident, a relative of a female PKK member imprisoned at Gebze Closed Prison said male prisoners held for non-political crimes attacked and injured several PKK women. The relative told Free Radio the women were told by prison administrators they could not quell the patriotic feelings of the men.
Nine women allegedly were injured when attacked with knives and sticks.
Justice Minister Mehmet Ali Sahin said an investigation determined there was no mistreatment.