A former commando of the Punjab Police's Elite Force, convict Mumtaz Qadri killed Taseer in January 2011, in an upmarket locality of Islamabad for allegedly criticising the controversial blasphemy laws.
He was arrested and tried by anti-terrorism court which awarded him death sentence same year. He then challenged the ruling in Islamabad High Court.
The Islamabad High Court earlier this year rejected Qadri's appeal against his death sentence under the Pakistan Penal Code (PPC) but accepted his application to void the Anti-terrorism Act's (ATA).
However, in March, the execution of all convicts was announced.
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Qadri made final appeal in the Supreme Court where a three-member bench headed by Justice Asif Saeed Khosa rejected his appeal and also rejected the Islamabad High Court decision to remove clauses of terrorism in the case.
It means that he is now convicted under both the PPC and anti-terrorism laws.
The court rejected the plea by Qadri's lawyer that blasphemy was a religious issue and anyone can take action if his religious sentiments were hurt.
Taseer was shot dead after he criticised the blasphemy laws following a visit to Asia Bibi, a Christian women convicted of blasphemy.
After the Supreme Court verdict, fate of Qadri has almost been sealed but he still has a thin ray of hope as he can file mercy appeal with the president of Pakistan.
He would be hanged if the mercy appeal is rejected and the president is bound to take consent of the relatives of the victim before pardoning a killer.
The controversial law was introduced by former military dictator Zia-ul Haq in 1980s and so far hundreds of people have been charged under them.