The words "revenge" and "price tag" were sprayed on some of the tombstones in the Muslim cemetery located in Mamilla opposite the capital's Independence Park, Army Radio reported Sunday.
Police said they were unsure when the tombstones were defaced, adding the incident could have occurred some weeks ago, Ynetnews.com said..
The discovery was made days after unknown assailants torched a Palestinian home in the village of Sinjil near Ramallah. Five members of the Palestinian family, including children were treated for smoke inhalation. The assailants scrawled "revenge" on exterior walls of the home and the name of the Israeli soldier Eden Attias, who was fatally stabbed in a bus in Afula by a Palestinian teenager last week.
Price tag refers to acts of violence by extremist settlers against Palestinians or Palestinian property and in some cases against Israeli security forces.
Israeli government officials have said such acts should be viewed as acts of terror and treated accordingly.