Although he would not ban shechita or halal slaughter outright, he told MPs last year that he believed “major improvements” could be made.
He also queried the view of Shechita UK, the kosher meat defence organisation, over how long it took for an animal to lose consciousness after shechita.
One option could be simply to ban the “non-stunned slaughter of bovine” animals, he stated.
Another would be to require “post-stunning” after the slaughter cut - for which there was “some rabbinical support”.
Mr Eustice has also raised the question of labelling meat produced by religious methods of slaughter which enters the general food market.
“The simplest way would be to label meat as unstunned, because that is a clearly definable legal definition,” he said last year.
But he noted this would cause “some concerns” for Jewish communities.
Congratulating Mr Eustice on his appointment, Shechita UK’s campaign director Shimon Cohen said the new Environment Secretary had “made no secret of his views on shechita and on Shechita UK.
“However, we look forward to a constructive dialogue with every confidence that as a member of the cabinet, he will support the pledge that this Government has already given us to maintain the longstanding commitment to the protection of religious animal slaughter for food.”
Mr Cohen expressed gratitude to Mr Eustice’s predecessor Theresa Villiers who had been “a great friend of our community. We are sorry to see her go.”