"We are not going to entertain this petition. We are very sorry," a bench comprising Chief Justice H L Dattu and Justice Amitava Roy said.
"We cannot close our eyes to centuries old traditions followed by the people. We cannot be examining these issues ... There has to be balance and harmony among all kinds of faiths," it said.
The court was hearing the PIL, filed by V Radhakrishnan who is associated with a Tamil Nadu based NGO, seeking striking down of Section 28 of the Prevention of Cruelty to Animals Act.
At the outset, the bench said that the Act itself gives the right to such religious practices.
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Senior advocate Raju Ramchandran, appearing for the NGO, sought "dispassionate" hearing of the PIL and said that irrespective of religion, proper procedures are required to be followed to ensure that no pain is inflicted on animals to be sacrificed.
The NGO, Makkal Mandram or Indian Citizens Forum, had relied on a recent letter of the Animal Welfare Board asking state governments to prevent camel slaughter during Bakr-Id.