Salman Taseer was the Governor of Punjab when he was shot dead in 2011 by Mumtaz Qadri, one of his body guards.
Qadri told police that he killed Mr Taseer because of his opposition to Pakistan's blasphemy law, which is sometimes used to persecute Christians.
The governor was a vocal critic of the death sentence given to Christian woman Asia Bibi who is accused of blasphemy against Islam.
Qadri's lawyer urged Islamabad High Court to overturn his conviction and release him. He spoke about the need to protect Islam and the blasphemy law.
Judges were asked to refer the case to the Federal Shariah Court because lawyers claimed it was a religious issue.
State prosecutors told the court the case had worldwide attention and releasing the governor's killer would darken the reputation of Pakistan.
Rejecting the appeal Justice Shaukat said: "Saying the blasphemy law is a black law and opposition against it would come under the domain of blasphemy."
But he added: "Nothing at all could justify the extra-judicial murder of any victim."
Wilson Chowdhry, Chairman of the British Pakistani Christian Association, said: "A few years ago we had more faith in the Pakistani legal system in the High and Supreme courts.
"However, a raft of poor decisions have eroded that trust. Extremists now yield power over the higher and lower courts, considering the failure of Asia's High Court Appeal.
"The loss of this appeal hearing for Mumtaz Qadri, will no doubt redouble efforts to see Asia Bibi's Supreme court Appeal fail.
"If this is the case it would take a brave Prime Minister to free Asia Bibi by Presidential Pardon, however, this is a duty the leader of a nation should commit himself too despite external pressures.
"Justice must be seen to be done or international scrutiny will increase."