Mumtaz Qadri was sentenced for killing Salman Taseer outside an upmarket coffee shop in Islamabad in 2011.
Qadri has admitted shooting Taseer, saying he objected to the politician’s calls to reform strict blasphemy laws which can carry the death penalty.
Around 300 of Qadri’s supporters chanted slogans calling for his release as a two-judge bench at Islamabad High Court began hearing the appeal.
At his original trial, Qadri was showered with rose petals by some lawyers. His current appeal team features two judges, including the former chief justice of Lahore High Court.
Outside the court, protesters wearing shirts with the logo of religious movement Pakistan Sunni Tehreek shouted “The lock of the prison will break, Qadri will be released!” and “Be ashamed, release Qadri!”
Malik Muhammad Safeer, Qadri’s brother, urged his release.
“My brother has done nothing wrong. He is happy and satisfied in the prison and always prays to God. Salman Taseer was killed because he committed blasphemy,” he told AFP.
Defence lawyers said they expect the appeal to be decided within weeks.
Pakistan lifted a moratorium on executions in terror cases in December after Taliban gunmen massacred 150 people at a school.
But executing someone convicted of murdering a “blasphemer” would risk a backlash from hardline religious groups and even more moderate public opinion.
After Qadri was convicted in 2011, dozens of furious lawyers ransacked the courtroom of the judge who had sentenced him to death. -AFP