The FSA said it was too difficult for individual abattoirs to keep a tally of how many animals were slaughtered without pre-stunning, the method required by shechita and halal.
It promised it would make a count but had not determined when it would do so.
But the British Veterinary Association, which argues that slaughter without pre-stunning is inhumane, said the FSA should provide regular updates on how many animals were killed.
Sean Wensley, the BVA president, told the Sunday Times that his organisation wanted an “absolute assurance” that the numbers would be made available.
Under EU rules, all animals slaughtered must be pre-stunned, but meat produced as kosher or halal is exempted.