The foundation for the future memorial to Egyptian protesters killed in the country's uprising and more than two-and-a-half years of turmoil has been damaged in Cairo's famed Tahrir Square.

Unknown assailants attacked, chipped away and sprayed graffiti on the huge stone early on Tuesday, just hours after it was inaugurated by the country's interim prime minister.

The overnight attack underscores the deep divisions plaguing this Arab nation since the 2011 uprising that toppled autocrat Hosni Mubarak.

Monday's inauguration came on the eve of the second anniversary of some of the fiercest confrontations between Egyptian protesters and security forces on a street near Tahrir, in which at least 45 people were killed by police.

New rallies are expected later in the day and there are fears of more unrest and clashes.