Revd Emmanuel Lorrian was speaking after around 50,000 mourners gathered for the funeral of Mumtaz Qadri in Rawalpindi, a city close to Islamabad.
Qadri was sentenced to death for the murder of Salman Taseer in 2011, a politician who strongly opposed the country's blasphemy laws often used to target Christians and other minorities.
He shot Mr Taseer in broad daylight while acting as a personal body guard. It was reported that he didn't show any remorse for his actions.
Qadri was hung on Monday for the crime.
The original sentence and hanging prompted mass protests across Pakistan, with many Muslims seeing Mumtaz Qadri as a hero.
Tens of thousands of policemen have been deployed across the country in response.
Fears have been expressed that Christians and churches may be attacked in the riots, but so far things have been relatively peaceful.
Revd Emmanuel confirmed this on Premier's News Hour: "Well there is no such situation at the moment because Christians have nothing to do with this. It's the court of our country and the law of the land.
"Since in the past the Christians had to pay all sorts of prices due to one case or the other, the Christians have a little bit of fear in their minds.
"There are fears that there will be more protests which could be violent. They are being violent and in the days to come more violence can take place."
