“My concern is to keep the animal suffering as low as possible,” Mr Waldhäusl said in a translation of a post on Facebook.
“Therefore, I have the strictest possible interpretation of the law examined. [This] is not about the creation of lists.”
On Thursday, Austria’s ambassador to Israel quoted Austrian Parliament Speaker Wolfgang Sobotka as saying “the idea of registering consumers is in no way compatible with the constitutionally guaranteed freedom of religion - it will not happen”.
“Shechita and Brit Milah are the cornerstones of Jewish life wherever Jews reside,” Mrs van der Zyl said in a statement on Friday.
“Therefore, I am deeply concerned about the situation regarding religious slaughter and I am also appalled about the proposed register of Jews who intend to buy kosher meat in Austria.
“This step reminds us of one of our Jewish history’s darkest chapters. We will be writing to Austria’s Ambassador in the UK to express our concern at these issues.”

In a separate reference to Nazism, the American Jewish Committee tweeted in German: “Soon with a star on the chest?”
Muslim communities in Austria have also expressed outrage at Mr Waldhäusl’s proposals.
The far-right FPÖ has been a partner in Austria's national coalition government since last year's parliamentary election, prompting an Israeli boycott of the ministries it controls.