Pakistani police say an an axe-wielding officer killed a Shia man in police custody, claiming he had committed blasphemy by insulting companions of the Prophet Muhammad.

Officer Mukhtar Ahmed said the incident took place at a police station in the city of Gujrat in eastern Punjab province early on Thursday.

Ahmed said the killer, officer Sarfraz Naveed, was questioning Syed Tufail Hyder who was detained on Wednesday following a street fight.

He added that Naveed killed Hyder with an axe, gave himself up and said he did it because Hyder allegedly repeatedly insulted companions of the Prophet during questioning.

Thursday's incident came days after a mob killed a young Christian couple and burned their bodies in a brick kiln where the man and his wife worked, claiming they had allegedly desecrated the Quran.