It follows a backlash from animal welfare organisations and members of the public who say live export is "inhumane".
Cornwall Park management says it has reviewed its decision to support the breeding programme.
Live exports of cows came under scrutiny last year when live export ship Gulf Livestock 1 capsized and sank off the coast of China.
The tragedy saw 5,867 New Zealand cows drown and 41 crew members, including two New Zealanders, lost at sea.
For nearly two years, MPI has been reviewing the controversial live export trade, which resumed after improvements to animal welfare standards were made.
