"Jumps races are a lottery for the horses, with a much higher rate of injuries and casualties than flat racing. This is due to horses being forced into jumping barriers at speed - something they would never do naturally."
Safe has been monitoring casualties and Mr Pryor said the death rate was unacceptable.
"On average one horse died per month this season. How can jumps racing be called a sport when it is routinely sending horses to an early death?"
Mr Pryor said there could have been deaths off the track that were not recorded in the stewards' reports, after a race, or in the trials.
"It is likely that the true animal welfare cost of the jumps racing industry is even greater."
He said the industry did not want the public to know that horses were regularly dying on New Zealand race tracks.
Mike Godber, who is the general manager of the racing integrity unit, which sets the regulations, said the racing industry did all it could to ensure the safety of the horses, including having two veterinarians and a staffed ambulance at every jumping race in case of an accident. Any horse which had not raced for six months was inspected by a vet.
He said the jumps racing season ran from May to the end of September and there was no evidence that there were deaths off the track not being recorded.
"I don't know of any horse that has been taken home and put down," Mr Godber said.
New Zealand Thoroughbred Racing company secretary Simon Cooper said there was no intention to stop jumps racing.
Mr Cooper said the question to be asked was what was an acceptable number of deaths. It was likely Safe wanted zero deaths but that was unrealistic.
"There are going to be fatalities in sport. The rate of fatalities in horse racing in New Zealand is one in every 2026 starts which is one of the best records in the world."
Mr Cooper did not agree that horses were being forced to jump barriers at speed. He said a horse was an animal of flight and it was natural for them to run and jump over obstacles.