Asad Shah, 40, was found with serious injuries outside his store last month and was pronounced dead at hospital.
Police described the killing as "religiously prejudiced".
Shah, an Ahmadi Muslim who moved to Glasgow from Pakistan in 1998, had recently posted a message on Facebook wishing people a happy Easter, "especially to my beloved Christian nation".
Tanveer Ahmed, 32, from Bradford in northern England, appeared at a preliminary court hearing in Glasgow today and afterwards issued a statement through his lawyer admitting his guilt.
"If I had not done this others would and there would have been more killing and violence in the world.
"I wish to make it clear that the incident was nothing at all to do with Christianity or any other religious beliefs -- even although I am a follower of the Prophet Muhammad peace be upon him I also love and respect Jesus Christ."
The legal process against Ahmed, who is also a Muslim and is being held in custody, will continue. The date for his next court hearing has not yet been set.
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