Mr Zaki and other campaigners had filed a court case charging Abdul Aziz with incitement to hatred and violence against the Shia minority.
The case was brought in response to the cleric’s refusal to condemn attacks such as that on a school in Peshawar in 2014 in which 152 people, most of them schoolchildren, were killed.
Mr Zaki was an editor of the website “Let us Build Pakistan”, which condemns sectarianism and is seen as promoting democratic and progressive values.
He is a prominent Pakistani journalist and human rights activist. Khurram Zaki.
While Mr Zaki was dining in a restaurant in the city’s north,he has been shot dead by suspects who came in motorbikes, reports said.
The spokesman for a splinter group of the Pakistani Taliban has said they were behind the shooting.
He said they killed him because of his recent campaign against a cleric of the Red Mosque in Islamabad.