Officials said the graffiti was discovered after an activist organization held a rally Saturday night at the Peace and Justice Plaza in Chapel Hill.
Some of the profanity-laced messages called for harming police officers and others for "jihad."
Chatham and Orange counties District Attorney Jeff Nieman called the vandalism "despicable."
"Calls for violence and murder have no place in this community, and we should all denounce it in the strongest possible terms," Nieman said.
No arrests have been made.
"Law enforcement officers risk their lives every day to keep all of us safe, including the individuals at this rally and those who spray-painted these hateful messages," Nieman added, "I only hope those responsible can be identified so they can be held accountable in court. I encourage anyone with information about the perpetrators to contact their local law enforcement agency."