Both the Muslim Council for Scotland and the Scottish Council of Jewish Communities have criticised the British Veterinary Association (BVA) publicity drive.
The campaign - which was stepped up last week when letters were sent to Scotland's political leaders - is at odds with Muslim and Jewish beliefs over halal and kosher practices. It has led to claims by the Muslim Council that a change could diminish Islamic observance.
Council board member Dr Salah Beltagui said: "It's an important part of our religion that the meat we eat should be killed and prepared in a certain way.
"The slaughter should be done with a very sharp knife which swiftly cuts all the veins in the throat. Once the blood is drained from the brain, the animal cannot feel anything. We believe this is more humane than stunning and it's a requirement for our religion. Unstunned animal slaughter must be retained for religious observance."
A spokeswoman for the Scottish Council of Jewish Communities added the shechita method of slaughter for kosher meat is humane in that it causes instant and unconsciousness. She added: "Research by the European Food Safety Authority indicatesd 31 per cent of cattle are not correctly stunned which causes unnecessary suffering. The kosher method ensures that never happens."
However, claims over reduced animal suffering are at odds with the views of the Farm Animal Welfare Council (FAWC), which believes the cut to the neck causes "significant pain and distress".
It also claims there is a delay to the animal becoming insensible - five to 10 seconds for sheep and 22 to 40 seconds for cows.
More than 80 per cent of halal meat in the UK is stunned, while all kosher meat is unstunned. Very little non-stunning takes place in Scotland, but the BVA has raised concerns meat produced this way may be on supermarket shelves north of the Border without consumers knowing.
It is calling for clearer labelling on meat and poultry, detailing how the animal was killed. This has been backed by the Muslim Council, who believe it would also help the Islamic community to be certain of what they are eating.
Dr Beltagui said: "We would welcome calls for clearer labelling, properly regulated and controlled. It would provide information for us about whether the meat has been slaughtered in the correct way and it would provide information for consumers so they can make a choice."
The Jewish Council says it would also accept clearer labelling.
The BVA e-petition on the UK Government's website, has attracted more than 72,000 signatures so far. The Scottish Government is examining food labelling and has said it will consider the inclusion of how animals are slaughtered. The European Commission is also looking at similar matters.
BVA president Robin Hargreaves said: "Our campaign on non-stun slaughter has always been exclusively driven by our members' concern for animal welfare, based on the scientific evidence. There is ample evidence to show unconsciousness is not instantaneous and that animal welfare is compromised if the animal is not stunned.
"While our position remains that every animal should be stunned before slaughter, if this is not possible we have been calling for clearer labelling to differentiate between stunned and non-stunned products. "