In 2011 Mumtaz Qadri, pictured, was found guilty of killing Salman Taseer after he had supported the case of Asia Bibi who became a victim of the country's blasphemy laws.
He's now appealing the verdict with anti-persecution group CLAAS warning that Islamists will attempt to pressure the judge into freeing him.
The group claims the original sentencing judge had to flee the country after receiving death threats.
Justice Shaukat Siddiqui has said that the court was ready for day-to-day hearings but the prosecution asked for more time to prepare and he was granted one more week.
Nasir Saeed, Director CLAAS-UK said that this is a very challenging case for the government and for the court too.
The court has said it is afraid of hearing of this case as there will be a lot of pressure from the Islamists who protested after the initial sentence, he said.
He added: "There many lawyers and a few judges who support Qadri and even if his supporters are not allowed in the court room, they can gather in the court yard.
"It is going to be difficult for the government and for judges but justice has to done."